https://peda.net/id/c435b218c55 2018-10-01T12:45:44+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/2c6c1fbac70 2018-10-03T15:02:17+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B2%5Cright)%5E2%3D%5Cleft(x-4%5Cright)%5Cleft(x%2B4%5Cright)" alt="\left(x+2\right)^2=\left(x-4\right)\left(x+4\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B4x%2B4%3Dx%5E2-16" alt="x^2+4x+4=x^2-16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%3D-20" alt="4x=-20"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-5" alt="x=-5"/><!--filtered attribute: style="display: inline;"--><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B5%5Cright)%5E2-%5Cleft(x-2%5Cright)%5E2%3D0" alt="\left(x+5\right)^2-\left(x-2\right)^2=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B10x%2B25-%5Cleft(x%5E2-4x%2B4%5Cright)%3D0" alt="x^2+10x+25-\left(x^2-4x+4\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B10x%2B2%3Dx%5E2-4x%2B4" alt="x^2+10x+2=x^2-4x+4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6x%3D2" alt="6x=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B1%7D%7B3%7D" alt="x=\frac{1}{3}"/> 2018-10-03T15:02:17+03:00 https://peda.net/id/d7942d66c6f 2018-10-03T13:48:20+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=6%5Ccdot4%2B1%3D25%3D5%5E2" alt="6\cdot4+1=25=5^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3%5Ccdot1%2B1%3D4%3D2%5E2" alt="3\cdot1+1=4=2^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=8%5Ccdot6%2B1%3D49%3D7%5E2" alt="8\cdot6+1=49=7^2"/><br/> väite näyttää pitävän paikkansa<br/> b) <br/> merkitään toista lukua kirjaimella n<br/> <div><img src="https://math-demo.abitti.fi/math.svg?latex=n(n%2B2)%2B1%3D(n-1)%5E2" alt="n(n+2)+1=(n-1)^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=n%5E2%2B2n%2B1%3D%5Cleft(n%2B1%5Cright)%5E2" alt="n^2+2n+1=\left(n+1\right)^2"/><br/> <br/> </div> tulos on n+1 neliö, n+1 on kokonaisluku joten väite pitää paikkansa 2018-10-03T13:48:20+03:00 https://peda.net/id/fca83f36c60 2018-10-02T08:21:16+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B2%5Cright)%5E2%3D%5Cleft(x-4%5Cright)%5Cleft(x%2B4%5Cright)" alt="\left(x+2\right)^2=\left(x-4\right)\left(x+4\right)"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B2%5Ccdot%20x%5Ccdot2%2B2%5E2%3Dx%5E2-4%5E2" alt="x^2+2\cdot x\cdot2+2^2=x^2-4^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B4x%2B4%3Dx%5E2-16" alt="x^2+4x+4=x^2-16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-x%5E2%2B4x%3D-16-4" alt="x^2-x^2+4x=-16-4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%3D-20" alt="4x=-20"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-5" alt="x=-5"/><br/> b) 2018-10-02T08:21:16+03:00 https://peda.net/id/91022316c56 2018-10-01T14:10:12+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(2x%2B5%5Cright)%5Cleft(2x-5%5Cright)%3D0" alt="\left(2x+5\right)\left(2x-5\right)=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%5E2-25%3D0" alt="4x^2-25=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%5E2%3D25" alt="4x^2=25"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%3D5" alt="2x=5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D2%7B%2C%7D5" alt="x=2{,}5"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B3%5Cright)%5Cleft(x-3%5Cright)%3D16" alt="\left(x+3\right)\left(x-3\right)=16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-9%3D16" alt="x^2-9=16"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D25" alt="x^2=25"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D5" alt="x=5"/> 2018-10-01T14:10:12+03:00 https://peda.net/id/cef5e8f4c56 2018-10-01T13:53:17+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-4x%2B4%3D0" alt="x^2-4x+4=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-2x%2B2%3D0" alt="x-2x+2=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%3D-2" alt="-x=-2"/><br/> x=2<br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-4x%2B4%3D1" alt="x^2-4x+4=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-2x%2B2%3D1" alt="x-2x+2=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%3D-1" alt="-x=-1"/><br/> x=1 ja 3<br/> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-4x%2B4%3D4" alt="x^2-4x+4=4"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x-2x%2B2%3D2" alt="x-2x+2=2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=-x%3D0" alt="-x=0"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D0" alt="x=0"/> ja 4 2018-10-01T13:50:27+03:00 https://peda.net/id/16ef4142c56 2018-10-01T13:45:19+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B3%5Cright)%5Cleft(x-3%5Cright)%3Dx%5E2-3%5E2%3Dx%5E2-9" alt="\left(x+3\right)\left(x-3\right)=x^2-3^2=x^2-9"/><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=x%3D3" alt="x=3"/><!--filtered attribute: style="display: inline;"--><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B7%5Cright)%5Cleft(x-7%5Cright)%3Dx%5E2-7%5E2" alt="\left(x+7\right)\left(x-7\right)=x^2-7^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D49" alt="x^2=49"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D7" alt="x=7"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B1%5Cright)%5Cleft(x-1%5Cright)%3Dx%5E2-1%5E2" alt="\left(x+1\right)\left(x-1\right)=x^2-1^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%3D1" alt="x^2=1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D1" alt="x=1"/> 2018-10-01T13:45:19+03:00 https://peda.net/id/7e838eb8c56 2018-10-01T13:41:03+03:00 a) <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B2%5Ccdot2x%2B4%3D%5Cleft(x%2B2%5Cright)%5E2" alt="x^2+2\cdot2x+4=\left(x+2\right)^2"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2%5Ccdot8x%2B64%3D%5Cleft(x-8%5Cright)%5E2" alt="x^2-2\cdot8x+64=\left(x-8\right)^2"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2%2B2%5Ccdot9x%2B81%3D%5Cleft(x%2B9%5Cright)%5E2" alt="x^2+2\cdot9x+81=\left(x+9\right)^2"/> 2018-10-01T13:41:03+03:00 https://peda.net/id/636f34bcc56 2018-10-01T13:25:59+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D4x%5E2-24x%2B36%3D20" alt="f\left(x\right)=4x^2-24x+36=20"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-8x%2B9%3D5" alt="x^2-8x+9=5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2x%5Ccdot3%2B3%5E2" alt="x^2-2x\cdot3+3^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=a%3Dx" alt="a=x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=b%3D3" alt="b=3"/><!--filtered attribute: style="display: inline;"--><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-3%5Cright)%5E2%3D5" alt="\left(x-3\right)^2=5"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(x-3%5Cright)%5E2%7D%3D%5Csqrt%7B5%7D" alt="\sqrt{\left(x-3\right)^2}=\sqrt{5}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Csqrt%7B5%7D%2B3" alt="x=\pm\sqrt{5}+3"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-12x%2B36%3D-1" alt="x^2-12x+36=-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%5E2-2x%5Ccdot6%2B6%5E2" alt="x^2-2x\cdot6+6^2"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-6%5Cright)%5E2%3D-1" alt="\left(x-6\right)^2=-1"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csqrt%7B%5Cleft(x-6%5Cright)%5E2%7D%3D%5Csqrt%7B-1%7D" alt="\sqrt{\left(x-6\right)^2}=\sqrt{-1}"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cpm%5Csqrt%7B-1%7D%2B6" alt="x=\pm\sqrt{-1}+6"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=ei%5C%20voi%5C%20ottaa%5C%20neli%C3%B6juurta%5C%20negatiivisesta" alt="ei\ voi\ ottaa\ neliöjuurta\ negatiivisesta"/><!--filtered attribute: style="display: inline;"--> 2018-10-01T13:25:59+03:00 https://peda.net/id/59e7ecb6c56 2018-10-01T13:04:14+03:00 a)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B3%5Cright)%5E2%3Dx%5E2%2B6x%2B9" alt="\left(x+3\right)^2=x^2+6x+9"/><br/> b)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x-2%5Cright)%5E2%3Dx%5E2-4x%2B4" alt="\left(x-2\right)^2=x^2-4x+4"/><br/> c)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(x%2B5%5Cright)%5E2%3Dx%5E2%2B10x%2B25" alt="\left(x+5\right)^2=x^2+10x+25"/><br/> d)<br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Cleft(7-x%5Cright)%5E2%3D49-14x%2Bx%5E2%3Dx%5E2-14x%2B49" alt="\left(7-x\right)^2=49-14x+x^2=x^2-14x+49"/> 2018-10-01T13:04:14+03:00