根号题求值,
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根号题求值,
![](http://img.wesiedu.com/upload/8/6e/86ed83db6f0829f5525b1e92f703e8e4.jpg)
![](http://img.wesiedu.com/upload/8/6e/86ed83db6f0829f5525b1e92f703e8e4.jpg)
![根号题求值,](/uploads/image/z/16230200-32-0.jpg?t=%E6%A0%B9%E5%8F%B7%E9%A2%98%E6%B1%82%E5%80%BC%2C%26nbsp%3B)
∵x+√(7y)=√14、y+√(7x)=√14,∴两式相减,得:(x-y)-√7(√x-√y)=0,
∴(√x+√y)(√x-√y)-√7(√x-√y)=0,又x、y不等,∴√x+√y=√7.
∵x+√(7y)=√14、y+√(7x)=√14,∴两式相加,得:(x+y)+√7(√x+√y)=2√14,
∴(x+y)+7=2√14,∴x+y=2√14-7.
由√x+√y=√7,得:x+y+2√(xy)=7,∴2√14-7+2√(xy)=7,∴√(xy)=7-√14.
∴x^(-1/2)+y^(-1/2)
=1/√x+1/√y=(√x+√y)/√(xy)=√7/(7-√14)=1/(√7-√2)=(1/5)(√7+√2).
∴(√x+√y)(√x-√y)-√7(√x-√y)=0,又x、y不等,∴√x+√y=√7.
∵x+√(7y)=√14、y+√(7x)=√14,∴两式相加,得:(x+y)+√7(√x+√y)=2√14,
∴(x+y)+7=2√14,∴x+y=2√14-7.
由√x+√y=√7,得:x+y+2√(xy)=7,∴2√14-7+2√(xy)=7,∴√(xy)=7-√14.
∴x^(-1/2)+y^(-1/2)
=1/√x+1/√y=(√x+√y)/√(xy)=√7/(7-√14)=1/(√7-√2)=(1/5)(√7+√2).