Question

If x + 1/2x = 5 then the value of x^2 + 1/4x^2 is ​

Answer 1

$\sf x + \frac{1}{2x} = 5$

$\sf \purple{squaring \: on \: both \: sides}$

$\implies (x + \frac{1}{2x} ) ^{2} = 5 ^{2}$

$\implies {x}^{2} + \frac{1}{4x ^{2} } + 2(x)( \frac{1}{2x} ) = 25$

$\implies {x}^{2} + \frac{1}{4x ^{2} } + 1= 25$

$\implies {x}^{2} + \frac{1}{4x ^{2} } = 25 - 1$

$\orange{ \therefore {x}^{2} + \frac{1}{4x ^{2} } = 24}$

HOPE IT HELPS!!