Question

Solve :- $x-7\sqrt{x}+12=0$

Short answer

Solution for equation will be -

• $x=16$
• $x=9$
  

Step-by-step solution

Step 1.  Given Data

Quadratic Equation - $x-7\sqrt{x}+12=0$

Step 2.  To Find

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

Step 3.  Explanation

Let the value of $\sqrt{x}=u$

Then the equation is -

$x-7\sqrt{x}+12=0$

${\left(\sqrt{x}\right)}^2-7\sqrt{x}+12=0$

Put the value of $\sqrt{x}=u$

$u^2-7u+12=0$

$(u-4)(u-3)=0$

By using zero product property -

$u-4=0$, $u-3=0$

$u=4$, $u=3$

Step 4.  Calculation

Replace u with $\sqrt{x}$

$\sqrt{x}=4$, $\sqrt{x}=3$

Do square both side -

${\left(\sqrt{x}\right)}^2=4^2$, ${\left(\sqrt{x}\right)}^2=3^2$

$x=16$, $x=9$