Question

已知{(x²+y²)-(x-y)²+2y(x-y)}÷4y=1,求4x²-y

Answer 1

{(x²+y²)-(x-y)²+2y(x-y)}÷4y=1

{x²+y²-(x²-2xy+y²)+2xy-2y²}÷4y=1

{x²+y²-x²+2xy-y²+2xy-2y²}÷4y=1

{4xy-2y²}÷4y=1

2y{2x-y}÷4y=1

{2x-y}÷2=1

2x-y=2

4x/(4x²-y²)-1/(2x+y)

=4x/[(2x-y)(2x+y)]-(2x-y)/[(2x-y)(2x+y)]

=[4x-(2x-y)]/[(2x-y)(2x+y)]

=(4x-2x+y)/[(2x-y)(2x+y)]

=(2x+y)/[(2x-y)(2x+y)]

=1/(2x-y)

=1/2