Question

Solve :- $6x^{-2}-23x^{-1}+20=0$

Short answer

Solution for Equation will be -

• $x=\frac{2}{5}$
• $x=\frac{3}{4}$
  

Step-by-step solution

Step 1.   Given Data 

Quadratic Equation - $6x^{-2}-23x^{-1}+20=0$

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 -

$6x^{-2}-23x^{-1}+20=0$

role="math" localid="1645031655392" ${6\left(x^{-1}\right)}^2-23x^{-1}+20=0$

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

$6u^2-23u+20=0$

$(u-\frac{5}{2})(u-\frac{4}{3})=0$

By using zero product property -

$u-\frac{5}{2}=0$, $u-\frac{4}{3}=0$

Step 4.  Calculation

Replace u with $x^{-1}$

$x^{-1}=\frac{5}{2}$, $x^{-1}=\frac{4}{3}$

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

$x=\frac{2}{5}$, $x=\frac{3}{4}$