已知x+y=10,xy=24,求x^2+y^2

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已知x+y=10,xy=24,求x^2+y^2
已知x+y=10,xy=24,求x^2+y^2

已知x+y=10,xy=24,求x^2+y^2
x^2+y^2
=(x+y)^2-2xy
=10^2-2*24
=100-48
=52

完全平方公式：(a+b)²=a²+2ab+b²
x²+y²=(x+y)²-2xy=10²-2×24=100-48=52

x^2+y^2=(x+y)^2-2xy=10^2-2*24=100-48=52

(x+y)^2=100
x^2+y^2+2xy=100
x^2+y^2=100-2xy=100-48=52

x^2+y^2=(x+y)^2-2xy=100-48=52

x^2+y^2
=x^2+y^2+2xy-2xy
=(x+y)^2-2xy
=100-48
=52

(X+Y)^2=X^2+Y^2+2XY
所以：
x^2+y^2就＝（X+Y）^2-2XY
x^2+y^2就＝52

52啦

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