已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_____
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![已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_____](/uploads/image/z/620119-55-9.jpg?t=%E5%B7%B2%E7%9F%A5%3A%28a%2Bb%29%26%23178%3B%3D11%2C%28a-b%29%26%23178%3B%3D5%2C%E5%88%99a%26%23178%3B%2Bb%26%23178%3B%E7%9A%84%E5%80%BC%E7%AD%89%E4%BA%8E_____)
已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_____
已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_____
已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_____
(a+b)²=11,得:a²+b²+2ab=11
(a-b)²=5,得:a²+b²-2ab=5
两式相加,得:2(a²+b²)=16
所以:a²+b²=8
已知:(a+b)²=11,(a-b)²=5,则a²+b²的值等于_8_
(a+b)²+(a-b)²=(a²+2ab+b²)+(a²-2ab+b²)=2(a²+b²)=16 所以a²+b²=8
(a+b)^2-(a-b)^2
=4ab
=11-5
=6
ab=3/2
a²+b²
=(a+b)^2-2ab
=11-3
=8