Question

数学：先化简再求值 [（x²+y²）²-4x²y²]/（x²-y²）其中x=2 y=2/3

Answer 1

原式=(x²+y²+2xy)(x²+y²-2xy)/(x²-y²)
=(x+y)²(x-y)²/[(x+y)(x-y)]
=(x+y)(x-y)
=(2+2/3)(2-2/3)
=8/3*4/3
=32/9

Answer 2

原式=(x^4+2x^2y^2+y^4-4x^2y^2)/(x^2-y^2)
=(x^2-y^2)^2/(x^2-y^2)
=x^2-y^2
=(x+y)(x-y)
当x=2,y=2/3时
原式=8/3*4/3=32/9

Answer 3

[（x²+y²）²-4x²y²]/（x²-y²）其中x=2 y=2/3
=（x²-y²）²/（x²-y²）
=（x²-y²）
=(4-4/9)=32/9

Answer 4

[（x²+y²）²-4x²y²]/（x²-y²）
=[（x²+y²-2xy）（x²+y²+2xy）]/[（x-y）(x+y)]
=[(x-y)²(x+y)²]/[（x-y）(x+y)]

=（x-y）(x+y)
=(2-2/3)(2+2/3)
=7/4

Answer 5

[（x²+y²）²-4x²y²]/（x²-y²）
=(x^4+y^4+2x^2y^2-4X^2y^2)/（x²-y²）
=(x^4+y^4-2x^2y^2-)/（x²-y²）
=(x²-y²）²/（x²-y²）
=x²-y²
=4-4/9
=32/9