Question

Solve using inequalities x^-8x+7/4x^2-4x+1<0

Answer 1

Given,

$\longrightarrow\dfrac{x^2-8x+7}{4x^2-4x+1}<0$

Factorising numerator and denominator each,

$\longrightarrow\dfrac{x^2-x-7x+7}{4x^2-2x-2x+1}<0$

$\longrightarrow\dfrac{x(x-1)-7(x-1)}{2x(2x-1)-(2x-1)}<0$

$\longrightarrow\dfrac{(x-1)(x-7)}{(2x-1)(2x-1)}<0$

$\longrightarrow\dfrac{(x-1)(x-7)}{(2x-1)^2}<0$

Here the denominator $(2x-1)^2$ is always positive since it's something squared.

So the numerator should be negative for satisfying the inequality.

Therefore,

$\longrightarrow(x-1)(x-7)<0$

Solution to this inequality is,

$\longrightarrow\underline{\underline{x\in(1,\ 7)}}$

Thus solved!