https://peda.net/id/9a0e6f9ec7a 2018-10-04T10:24:59+03:00 https://peda.net/:static/535/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/084d22a2c7b 2018-10-08T13:03:43+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-4%5Cright)%5Cleft(x%2B2%5Cright)%3D-5" alt="\left(x-4\right)\left(x+2\right)=-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2x-8%3D-5" alt="x^2-2x-8=-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2x-8%2B9%3D-5%2B9" alt="x^2-2x-8+9=-5+9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2%5Ccdot1%5Ccdot%20x%2B1%3D4" alt="x^2-2\cdot1\cdot x+1=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B1%5Cright)%5E2%3D4" alt="\left(x+1\right)^2=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(x%2B1%5Cright)%5E2%7D%3D%5Csqrt%7B4%7D" alt="\sqrt{\left(x+1\right)^2}=\sqrt{4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%2B1%3D2" alt="x+1=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-3%5Cright)%5E2%3Dx-1" alt="\left(x-3\right)^2=x-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-3%5Cright)%5Cleft(x-3%5Cright)%3Dx-1" alt="\left(x-3\right)\left(x-3\right)=x-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-6x%2B9%3Dx-1" alt="x^2-6x+9=x-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-7x%2B10%3D0" alt="x^2-7x+10=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-7%5Cpm%5Csqrt%7B7%5E2-4%5Ccdot1%5Ccdot10%7D%7D%7B2%7D%3D%5Cfrac%7B-7%5Cpm%5Csqrt%7B49-40%7D%7D%7B2%7D%3D%5Cfrac%7B-7%2B3%7D%7B2%7D%3D-%5Cfrac%7B4%7D%7B2%7D%3D-2%5C%20tai%5C%20%5Cfrac%7B-7-3%7D%7B2%7D%3D-%5Cfrac%7B10%7D%7B2%7D%3D-5" alt="x=\frac{-7\pm\sqrt{7^2-4\cdot1\cdot10}}{2}=\frac{-7\pm\sqrt{49-40}}{2}=\frac{-7+3}{2}=-\frac{4}{2}=-2\ tai\ \frac{-7-3}{2}=-\frac{10}{2}=-5"/><br/> c)<br/> <br/> 2018-10-04T11:39:39+03:00 https://peda.net/id/148a0888c7b 2018-10-04T11:32:50+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%2B3x%2B1%3D0" alt="2x^2+3x+1=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-%5Cfrac%7B-3%5Cpm%5Csqrt%7B3%5E2-4%5Ccdot2%5Ccdot1%7D%7D%7B2%5Ccdot2%7D" alt="x=-\frac{-3\pm\sqrt{3^2-4\cdot2\cdot1}}{2\cdot2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-3%5Cpm%5Csqrt%7B1%7D%7D%7B4%7D%3D%5Cfrac%7B-3%5Cpm1%7D%7B4%7D" alt="x=\frac{-3\pm\sqrt{1}}{4}=\frac{-3\pm1}{4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-4%7D%7B4%7D%3D-1%5C%20tai%5C%20x%3D%5Cfrac%7B-2%7D%7B4%7D%3D-%5Cfrac%7B1%7D%7B2%7D" alt="x=\frac{-4}{4}=-1\ tai\ x=\frac{-2}{4}=-\frac{1}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=summa%5C%20on%5C%20-%5Cfrac%7Bb%7D%7Ba%7D%3D-%5Cfrac%7B3%7D%7B2%7D%7B%2C%7D%5C%20eli%5C%20-1%2B%5Cleft(-%5Cfrac%7B1%7D%7B2%7D%5Cright)" alt="summa\ on\ -\frac{b}{a}=-\frac{3}{2}{,}\ eli\ -1+\left(-\frac{1}{2}\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=tulo%5C%20on%5C%20%5Cfrac%7Bc%7D%7Ba%7D%7B%2C%7D%5C%20%5Cfrac%7B1%7D%7B2%7Deli%5C%20-1%5Ccdot%5Cleft(-%5Cfrac%7B1%7D%7B2%7D%5Cright)%3D%5Cfrac%7B1%7D%7B2%7D" alt="tulo\ on\ \frac{c}{a}{,}\ \frac{1}{2}eli\ -1\cdot\left(-\frac{1}{2}\right)=\frac{1}{2}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=summa%5C%20-%5Cfrac%7B3%7D%7B2%7D%3D-1%5C%20%5Cfrac%7B1%7D%7B2%7D%7B%2C%7D%5C%20tulo%5C%20%5Cfrac%7B7%7D%7B2%7D%3D3%5C%20%5Cfrac%7B1%7D%7B2%7D" alt="summa\ -\frac{3}{2}=-1\ \frac{1}{2}{,}\ tulo\ \frac{7}{2}=3\ \frac{1}{2}"/> 2018-10-04T11:32:50+03:00 https://peda.net/id/df249526c7a 2018-10-04T11:09:52+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%5E2%2B1%5Cright)%5E2%3D100" alt="\left(x^2+1\right)^2=100"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(x%5E2%2B1%5Cright)%5E2%7D%3D%5Csqrt%7B100%7D" alt="\sqrt{\left(x^2+1\right)^2}=\sqrt{100}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B1%3D10" alt="x^2+1=10"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D9" alt="x^2=9"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7Bx%5E2%7D%3D%5Csqrt%7B9%7D" alt="\sqrt{x^2}=\sqrt{9}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D3" alt="x=3"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%5E2-3x%5Cright)%5E2%3D%5Cleft(x%5E2-2%5Cright)%5E2%5C%20%5C%20%5C%20%5Cmid%5Csqrt%7B%20%7D" alt="\left(x^2-3x\right)^2=\left(x^2-2\right)^2\ \ \ \mid\sqrt{ }"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-3x%3Dx%5E2-2%5C%20%5Cmid-x%5E2" alt="x^2-3x=x^2-2\ \mid-x^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-3x%3D-2%5C%20%5Cmid%3A%5Cleft(-3%5Cright)" alt="-3x=-2\ \mid:\left(-3\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B2%7D%7B3%7D" alt="x=\frac{2}{3}"/> 2018-10-04T11:09:52+03:00 https://peda.net/id/449c0e3cc7a 2018-10-04T10:51:14+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-6x%2B9%3D100" alt="x^2-6x+9=100"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-3%5Cright)%5E2%3D100" alt="\left(x-3\right)^2=100"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(x-3%5Cright)%5E2%7D%3D%5Csqrt%7B100%7D" alt="\sqrt{\left(x-3\right)^2}=\sqrt{100}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-3%3D10" alt="x-3=10"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D13" alt="x=13"/><!--filtered attribute: style="display: inline;"--><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-6x%2B5%3D0" alt="x^2-6x+5=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-6x%3D-5" alt="x^2-6x=-5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2x%5Ccdot3%2B3%5E2%3D-5%2B3%5E2" alt="x^2-2x\cdot3+3^2=-5+3^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-3%5Cright)%5E2%3D4" alt="\left(x-3\right)^2=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(x-3%5Cright)%5E2%7D%3D%5Csqrt%7B4%7D" alt="\sqrt{\left(x-3\right)^2}=\sqrt{4}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-3%3D2" alt="x-3=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5" alt="x=5"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%2B12x%2B8%3D0" alt="2x^2+12x+8=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%5E2%2B2%5Ccdot2x%5Ccdot3%2B8%2B1%3D1" alt="2x^2+2\cdot2x\cdot3+8+1=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(2x%2B3%5Cright)%5E2%3D1" alt="\left(2x+3\right)^2=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(2x%2B3%5Cright)%5E2%7D%3D%5Csqrt%7B1%7D" alt="\sqrt{\left(2x+3\right)^2}=\sqrt{1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%2B3%3D1" alt="2x+3=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%3D-2" alt="2x=-2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-1" alt="x=-1"/> 2018-10-04T10:51:14+03:00 https://peda.net/id/8fffb0a6c7a 2018-10-04T10:53:22+03:00 <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-3" alt="x=-3"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-4x%3D-c" alt="x^2-4x=-c"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(-3%5Cright)%5E2-4%5Ccdot%5Cleft(-3%5Cright)%3D-c" alt="\left(-3\right)^2-4\cdot\left(-3\right)=-c"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=9%2B12%3D-c" alt="9+12=-c"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=c%3D-21" alt="c=-21"/><br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-4x-21%3D0" alt="x^2-4x-21=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=9%2B12-21%3D0" alt="9+12-21=0"/><br/> yhtälöllä ei ole toista ratkaisua 2018-10-04T10:39:01+03:00 https://peda.net/id/88620868c7a 2018-10-04T10:31:39+03:00 <div>a)</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=18x%5E2-24x%2B6%3D0" alt="18x^2-24x+6=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B24%5Cpm%5Csqrt%7B%5Cleft(24%5E2%5Cright)-4%5Ccdot18%5Ccdot6%7D%7D%7B2%5Ccdot18%7D" alt="x=\frac{24\pm\sqrt{\left(24^2\right)-4\cdot18\cdot6}}{2\cdot18}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B24%5Cpm%5Csqrt%7B144%7D%7D%7B36%7D" alt="x=\frac{24\pm\sqrt{144}}{36}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B24%2B12%7D%7B36%7D%5C%20tai%5C%20x%3D%5Cfrac%7B24-12%7D%7B36%7D" alt="x=\frac{24+12}{36}\ tai\ x=\frac{24-12}{36}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B36%7D%7B36%7D%3D1%5C%20tai%5C%20x%3D%5Cfrac%7B12%7D%7B36%7D%3D%5Cfrac%7B1%7D%7B3%7D" alt="x=\frac{36}{36}=1\ tai\ x=\frac{12}{36}=\frac{1}{3}"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5Cleft(x%2B2%5Cright)%3D%5Cfrac%7B1%7D%7B2%7D" alt="x\left(x+2\right)=\frac{1}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B2x-%5Cfrac%7B1%7D%7B2%7D%3D0" alt="x^2+2x-\frac{1}{2}=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B2%5E2-4%5Ccdot1%5Ccdot%5Cleft(-%5Cfrac%7B1%7D%7B2%7D%5Cright)%7D%7D%7B2%5Ccdot1%7D" alt="x=\frac{-2\pm\sqrt{2^2-4\cdot1\cdot\left(-\frac{1}{2}\right)}}{2\cdot1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B4-%5Cleft(-2%5Cright)%7D%7D%7B2%7D" alt="x=\frac{-2\pm\sqrt{4-\left(-2\right)}}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-2%5Cpm%5Csqrt%7B6%7D%7D%7B2%7D" alt="x=\frac{-2\pm\sqrt{6}}{2}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B-2%2B%5Csqrt%7B6%7D%7D%7B2%7D%5C%20tai%5C%20x%3D%5Cfrac%7B-2-%5Csqrt%7B6%7D%7D%7B2%7D" alt="x=\frac{-2+\sqrt{6}}{2}\ tai\ x=\frac{-2-\sqrt{6}}{2}"/></div> 2018-10-04T10:31:39+03:00