### Question 1

SSC-CGL 2020 Mar 4 Shift 1

If $\displaystyle 5x + \frac {1}{3x} = 4$, then $\displaystyle 9x^2 + \frac{1}{25x^2}$ =?

### Solution in Detail

Given $\displaystyle 5x + \frac {1}{3x} = 4$

With an eye on the required expression, multiply both sides by 3/5 to get

$\displaystyle \frac35 \times \bigg(5x + \frac {1}{3x} = 4\bigg)$

$\displaystyle \therefore 3x + \frac{1}{5x} = \frac{12}{5}$

$\displaystyle \therefore \bigg(3x + \frac{1}{5x}\bigg)^2 = \bigg(\frac{12}{5}\bigg)^2$

squaring and simplifying,

$\displaystyle 9x^2 + \frac 65 + \frac{1}{25x^2} = \frac{144}{25} $

$\displaystyle \therefore 9x^2 + \frac{1}{25x^2} = \frac{144}{25} -\frac65$

$\displaystyle = \frac{114}{25}\:\underline {Ans}$

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