十字相乘的.已知(2x²+2y²)(x²-2+y²)-16=0,求x的四次方+y的四次方+2x²y²的值.
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十字相乘的.已知(2x²+2y²)(x²-2+y²)-16=0,求x的四次方+y的四次方+2x²y²的值.
十字相乘的.已知(2x²+2y²)(x²-2+y²)-16=0,求x的四次方+y的四次方+2x²y²的值.
十字相乘的.已知(2x²+2y²)(x²-2+y²)-16=0,求x的四次方+y的四次方+2x²y²的值.
(2x²+2y²)(x²-2+y²)-16=0
2(x²+y²)(x²+y²-2)=16
(x²+y²)(x²+y²-2)=8
(x²+y²)²-2(x²+y²)=8
设x²+y²=t (t≥0)
则:
t²-2t=8
t²-2t-8=0
(t-4)(t+2)=0
t=4
t=-2(舍去)
所以:x²+y²=4
(x²+y²)²-2(x²+y²)=8
x⁴+y⁴+2x²y²-2(x²+y²)=8
x⁴+y⁴+2x²y²-8=8
x⁴+y⁴+2x²y²=16