已知:√x=√a+1/√a求(x2+x-6)/x÷(x+3)/(x2-2x)-[(x-2)+√(x2-4x)]/[(x-2)-√(x2-4x)]的值
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![已知:√x=√a+1/√a求(x2+x-6)/x÷(x+3)/(x2-2x)-[(x-2)+√(x2-4x)]/[(x-2)-√(x2-4x)]的值](/uploads/image/z/7149867-51-7.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E2%88%9Ax%3D%E2%88%9Aa%2B1%2F%E2%88%9Aa%E6%B1%82%EF%BC%88x2%2Bx-6%EF%BC%89%2Fx%C3%B7%28x%2B3%29%2F%28x2-2x%29-%5B%28x-2%29%2B%E2%88%9A%28x2-4x%29%5D%2F%5B%28x-2%29-%E2%88%9A%28x2-4x%29%5D%E7%9A%84%E5%80%BC)
已知:√x=√a+1/√a求(x2+x-6)/x÷(x+3)/(x2-2x)-[(x-2)+√(x2-4x)]/[(x-2)-√(x2-4x)]的值
已知:√x=√a+1/√a求(x2+x-6)/x÷(x+3)/(x2-2x)-[(x-2)+√(x2-4x)]/[(x-2)-√(x2-4x)]的值
已知:√x=√a+1/√a求(x2+x-6)/x÷(x+3)/(x2-2x)-[(x-2)+√(x2-4x)]/[(x-2)-√(x2-4x)]的值
√x=√a+1/√a
x=a+2+1/a
x-2=a+1/a
x^2-4x+4=a^2+2+1/a^2
x^2-4x=a^2-2+1/a^2
x^2-4x=(a-1/a)^2
(x^2+x-6)/x÷(x+3)/(x^2-2x)-[(x-2)+√(x^2-4x)]/[(x-2)-√(x^2-4x)]
=(x-2)(x+3)/x *x(x-2)/(x+3)-[((x-2)+√(x^2-4x))^2]/[(x-2)^2-(x^2-4x)]
=(x-2)^2-[(x-2)^2+2(x-2)√(x^2-4x)+x^2-4x]/[x^2-4x+4-x^2+4x]
=(x-2)^2-[x^-4x+4+2(x-2)√(x^2-4x)+x^2-4x]/4
=(x-2)^2-[x^2-4x+4-2+(x-2)√(x^2-4x)]/2
=(x-2)^2-[(x-2)^2-2+(x-2)√(x^2-4x)]/2
=(a-1/a)^2-[((a+1/a)^2-2+(a-1/a)√(a-1/a)^2]/2
=(a-1/a)^2-[(a+1/a)^2-2+(a-1/a)(a-1/a)]/2
=(a-1/a)^2-[a^2+2+1/a^2-2+a^2-2+1/a^2]/2
=a^2-2+1/a^2-[2a^2+2/a^2-2]/2
=a^2-2+1/a^2-a^2-1/a^2+1
=-1