若(a+b)²=17,(a-b)²=13,则a²+b²=_______,ab=_____
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![若(a+b)²=17,(a-b)²=13,则a²+b²=_______,ab=_____](/uploads/image/z/3942009-9-9.jpg?t=%E8%8B%A5%28a%2Bb%29%26%23178%3B%3D17%2C%28a-b%29%26%23178%3B%3D13%2C%E5%88%99a%26%23178%3B%2Bb%26%23178%3B%3D_______%2Cab%3D_____)
若(a+b)²=17,(a-b)²=13,则a²+b²=_______,ab=_____
若(a+b)²=17,(a-b)²=13,则a²+b²=_______,ab=_____
若(a+b)²=17,(a-b)²=13,则a²+b²=_______,ab=_____
a²+b²
=【(a+b)²+(a-b)²】÷2
=(17+13)÷2
=15
ab
=【(a+b)²-(a-b)²】÷4
=(17-13)÷4
=1
解
(a+b)²=17
即
a²+2ab+b²=17 ①
(a-b)²=13
即
a²-2ab+b²=13 ②
①+②得:
2a²+2b²=30
∴a²+b²=15
①-②得:
4ab=4
∴ab=1
a²+b²=15 ab=1