已知(a+b)²=4,(a-b)²=36,求a²+b²和ab的值
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已知(a+b)²=4,(a-b)²=36,求a²+b²和ab的值
已知(a+b)²=4,(a-b)²=36,求a²+b²和ab的值
已知(a+b)²=4,(a-b)²=36,求a²+b²和ab的值
(a+b)²=a²+b²+2ab=4
(a-b)²=a²+b²-2ab=36
相减得4ab=-32,ab=-8
所以a²+b²=4-2ab=20
a²+b² =1/2 *[(a+b)²+(a-b)²] =1/2 * 40=20
AB=1/4 *[(a+b)²-(a-b)²] =-8
(a+b)^2=4, (a-b)^2=36,
a²+2ab+b²=4 ① a²-2ab+b²=36②
①+②,得
2(a²+b²)=4+36
即a²+b²=20 2ab=4-(a²+b²)
所以ab=-8
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