x^2+2x-2=0
x1=-1+(1+2)^0.5=-1+(3)^0.5
x2=-1-(1+2)^0.5=-1-(3)^0.5
x^2+5x=7
x^2+5x-7=0
x1=-5/2+(25/4+7)^0.5=-5/2+(53)^0.5/2=(-5+(53)^0.5)/2
x2=-5/2-(25/4+7)^0.5=-5/2-(53)^0.5/2=(-5-(53)^0.5)/2
3x^2+5*(2x+1)=0
3x^2+10x+5=0
x1=(-10+(100-60)^0.5)/6=(-10+(40)^0.5)/6=(-5+(10)^0.5)/3
x2=(-10-(100-60)^0.5)/6=(-10-(40)^0.5)/6=(-5-(10)^0.5)/3
(2^0.5)x^2+4*(3^0.5)x-2*(2^0.5)=0
x^2+4*((3/2)^0.5)x-2=0
x1=-2*((3/2)^0.5)+(2*((3/2)^0.5)^2+2)^0.5=(-6^0.5)+(6+2)^0.5=(-3^0.5+3)*2^0.5
x2=-2*((3/2)^0.5)-(2*((3/2)^0.5)^2+2)^0.5=(-6^0.5)-(6+2)^0.5=(-3^0.5-3)*2^0.5
已知方程x平方+kx-6=0的是個根是2,求它的另一個根及k的值
x^2+kx-6=0
x1=-k/2+(k^2/4+6)^0.5=2
x2=-k/2-(k^2/4+6)^0.5
-k/2+(k^2/4+6)^0.5=2
(k^2/4+6)^0.5=2+k/2
k^2/4+6=(2+k/2)^2=4+2k+k^2/4
4+2k=6
2k=2
k=1
x2=-k/2-(k^2/4+6)^0.5=-1/2-(1/4+6)^0.5=-1/2-5/2=-3