已知(a+b)²=17,(a-b)²=13,求a²+b²与ab的值
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已知(a+b)²=17,(a-b)²=13,求a²+b²与ab的值
已知(a+b)²=17,(a-b)²=13,求a²+b²与ab的值
已知(a+b)²=17,(a-b)²=13,求a²+b²与ab的值
∵(a+b)²+(a-b)²=(a²+b²+2ab)+(a²+b²-2ab)=2a²+2b²=30
∴a²+b²=15
∵(a+b)²-(a-b)²=(a²+b²+2ab)-(a²+b²-2ab)=a²+b²+2ab-a²-b²+2ab=4ab=4
∴ab=1
(a+b)^2=a^2+2ab+b^2=289
(a-b)^2=a^2-2ab+b^2=169
两式相加得
2a^2+2b^2=458
a^2+b^2=229
两式相减4ab=120
ab=30