Question

If $\sqrt{1+\frac{55}{729}}=1+\frac{x}{27}$, then find x.

Answer 1

Squaring both sides :-

$1+\frac{55}{729}=1+\frac{x^2}{729}+\frac{2x}{27}$

$\Rightarrow 55=x^2+54x$

$\Rightarrow x^2+54x-55=0$

$\Rightarrow x^2+55x-x-55=0$

$\Rightarrow x(x+55)-1(x+55)=0$

$\Rightarrow (x-1)(x+55)=0$

So $x=1$ or $x=-55$

As square root function is always positive then we've $x=1$.