Question

Solve :- $8x^{-2}-10x^{-1}+3=0$

Short answer

Solution for Equation will be -

• $x=\frac{4}{3}$
• $x=2$
  

Step-by-step solution

Step 1.   Given Data

Quadratic Equation - $8x^{-2}-10x^{-1}+3=0$

Step 2.   To Find

We have to solve it and find the value of x.

Step 3.  Explanation

Let the value of $x^{-1}=u$

Then the equation is -

$8x^{-2}-10x^{-1}+3=0$

$8{\left(x^{-1}\right)}^2-10x^{-1}+3=0$

Put the value of $x^{-1}=u$

$8u^2-10u+3=0$

role="math" localid="1645030717473" $(u-\frac{3}{4})(u-\frac{1}{2})=0$

By using zero product property -

$u-\frac{3}{4}=0$, $u-\frac{1}{2}=0$

$u=\frac{3}{4}$, $u=\frac{1}{2}$

Step 4.  Calculation

Replace u with $x^{-1}$

$x^{-1}=\frac{3}{4}$, localid="1645030916197" $x^{-1}=\frac{1}{2}$

Solve for x by taking the reciprocal since $x^{-1}=\frac{1}{x}$

$x=\frac{4}{3}$, $x=2$