Question

If the square of twice a number is 9 more than thrice the square of the given number, then the number can be _____ .[ 2 marks]

Answer 1

Let the number be $x$.
$\text{Square of twice the number}=(2x{)}^2=4x^2$
$\text{Three times the square of the number}=3x^2$
[1 mark]

Given, square of twice the number is 9 more than three times the square of the number.
$\Rightarrow 4x^2=3x^2+9$
$\Rightarrow x^2-9=0$
$\Rightarrow x^2=9$
$\Rightarrow x=\pm 3$ [1 mark]