Question

初中数学题在线解答

化简求值：
(x-y+ X-y分之4xy)(x+y- x+y分之4xy),其中x=-2分之1，y=根号2.
(x-y+ x-y分之4xy)(x+y- x+y分之4xy),其中x=-2分之1，y=根号2.

Answer 1

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

∴ [x-y + (4xy)/(x-y)][x+y - (4xy)/(x+y)]=(x+y)²/(x-y) * (x-y)²/(x+y) = (x+y)(x-y)=x²-y²=(-1/2)²-(√2)²=1/4 - 2=-7/4

Answer 2

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

∴ [x-y + (4xy)/(x-y)][x+y - (4xy)/(x+y)]=(x+y)²/(x-y) * (x-y)²/(x+y) = (x+y)(x-y)=x²-y²=(-1/2)²-(√2)²=1/4 - 2=-7/4

Answer 3

变形为【x-(y-x-y分之4xy)】【（x+y-x+y分之4xy）】，可以逆用平方差公式
再带值进去算就可以了

Answer 4

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

∴ [x-y + (4xy)/(x-y)][x+y - (4xy)/(x+y)]=(x+y)²/(x-y) * (x-y)²/(x+y) = (x+y)(x-y)=x²-y²=(-1/2)²-(√2)²=1/4 - 2=-7/4

Answer 5

Y≈1.414

Answer 6

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