Advertisements
Advertisements
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
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
APPEARS IN
RELATED QUESTIONS
Solve the following equation for x:
`7^(2x+3)=1`
Solve the following equation for x:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Prove that:
`sqrt(1/4)+(0.01)^(-1/2)-(27)^(2/3)=3/2`
Solve the following equation:
`4^(x-1)xx(0.5)^(3-2x)=(1/8)^x`
Show that:
`((a+1/b)^mxx(a-1/b)^n)/((b+1/a)^mxx(b-1/a)^n)=(a/b)^(m+n)`
If `a=x^(m+n)y^l, b=x^(n+l)y^m` and `c=x^(l+m)y^n,` Prove that `a^(m-n)b^(n-l)c^(l-m)=1`
Write the value of \[\sqrt[3]{125 \times 27}\].
Which one of the following is not equal to \[\left( \sqrt[3]{8} \right)^{- 1/2} ?\]
If a, b, c are positive real numbers, then \[\sqrt{a^{- 1} b} \times \sqrt{b^{- 1} c} \times \sqrt{c^{- 1} a}\] is equal to
The value of \[\left\{ 8^{- 4/3} \div 2^{- 2} \right\}^{1/2}\] is
