### Question 2

SSC-CGL 2020 Mar 4 Shift 2

If $\displaystyle 30x^2 - 15x + 1 = 0$, then $\displaystyle 25x^2 + \frac{1}{36x^2}=?$

### Solution in Detail

Keep an eye on the expression to be found. It has $\displaystyle 5x$ and $\displaystyle \frac{1}{6x}$ in square form. Our effort will be to get these terms. It's not difficult. Now proceed like this and try to understand the trick:

Given $\displaystyle 30x^2 - 15x + 1 = 0$

Divide by $\displaystyle 6x$

$\displaystyle \therefore 5x - \frac{15}{6} + \frac{1}{6x} = 0$

$\displaystyle \therefore 5x + \frac{1}{6x} = \frac 52$

Squaring both sides,

$\displaystyle 25x^2 + 2\cdot \frac{5x}{6x} + \frac{1}{36x^2} = \frac{25}{4}$

$\displaystyle \therefore 25x^2 + \frac{1}{36x^2} = \frac{55}{12}\:\underline{Ans}$

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