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If x is very large as compare to y , the...

If `x` is very large as compare to `y ,` then prove that `sqrt(x/(x+y))dotsqrt(x/(x-y))=1+(y^2)/(2x^2)` .

Text Solution

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`sqrt((x)/(x+y)) sqrt((x)/(x-y)) = ((1)/(1+y/x))^(1//2)((1)/(1-y/x))^(1//2)`
`= (1-(y^(2))/(x^(2)))^(-1//2) = 1+1/2.^(y^(2))/(x^(2))`
(ignoring higher powers of `y//x` as `y//x rarr 0`)
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