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Question
If x = 2 and y = 4, then \[\left( \frac{x}{y} \right)^{x - y} + \left( \frac{y}{x} \right)^{y - x} =\]
Options
4
8
12
2
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Solution
We have to find the value of `(x/y)^(x-y) + (y/x)^(y-x) ` if x = 2, y = 4
Substitute x = 2, y = 4 in `(x/y)^(x-y) + (y/x)^(y-x) ` to get,
`(x/y)^(x-y) + (y/x)^(y-x) ` = `(2/4)^(2-4) + (4/2)^(4-2)`
= `(2/4)^-2+ (4/2)^2`
= `(1/2)^-2 + (2)^2`
= `(1/2^-2) + 4`
`(x/y)^(x-y) + (y/x)^(y-x) = 1/(1/2^2) +4`
=` 1/(1/4) +4`
= `1 xx 4/1 +4`
= 4+4
= 8
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