x²-x-3=0有两个实数根,且分别是x₁,x₂,求x₁²+x₂²
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x²-x-3=0有两个实数根,且分别是x₁,x₂,求x₁²+x₂²
x²-x-3=0有两个实数根,且分别是x₁,x₂,求x₁²+x₂²
x²-x-3=0有两个实数根,且分别是x₁,x₂,求x₁²+x₂²
x1+x2=1
x1x2=-3
所以x1²+x2²=(x1+x2)²-2x1x2
=1+6
=7
由方程得:
a=1 b=﹣1 c=﹣3
∴x₁+x₂=﹣b/a=1
x₁x₂=c/a=﹣3
x₁²+x₂²
=x₁²+x₂²+2x₁x₂-2x₁x₂
=﹙x₁+x₂﹚²-2x₁x₂
=1²-2×﹙﹣3﹚
=7