Question

Find the roots of the given equation
$16x-\frac{10}{x}=27$

Answer 1

Finding the roots of given equation :

Given equation $16x-\frac{10}{x}=27$
Both sides multiply by $x$, we get
$$\begin{gathered} \Rightarrow 16x^2-10=27x \\ \Rightarrow 16x^2-27x-10=0 \\ \Rightarrow 16x^2-(32-5)x-10=0 \\ \Rightarrow 16x^2-32x+5x-10=0 \\ \Rightarrow 16x(x-2)+5(x-2)=0 \\ \Rightarrow (16x+5)(x-2)=0 \\ \Rightarrow x=-\frac{5}{16},2 \end{gathered}$$

Hence the required roots are $-\frac{5}{16}\&2$