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If G is the geometric mean of xa n dy th...

If `G` is the geometric mean of `xa n dy` then prove that `1/(G^2-x^2)+1/(G^2-y^2)=1/(G^2)`

Text Solution

Verified by Experts

As given `G=sqrt(xy)`
`therefore1/(G^(2)-x^(2))+1/(G^(2)-y^(2))=1/(xy-x^(2))+1/(xy-y^(2))`
`=1/(x-y){-1/x+1/y}`
`=1/(xy)=1/(G^(2))`
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CENGAGE-PROGRESSION AND SERIES-Examples
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