Question

Solve the following quadratic equations by factorization method.
(i) y² – 3 = 0

Answer 1

Given: y² – 3 = 0
We can rewrite the given equation as:
$y^2-{\left(\sqrt{3}\right)}^2$=0
On using the identity (a² – b²) = (a + b)(a – b), we get:
$(y+\sqrt{3})(y-\sqrt{3})$=0
We know that if the product of two numbers is zero, then at least one of them must be zero.
Thus,
$$\begin{gathered} y+\sqrt{3}=0\mathrm{or}y-\sqrt{3}=0 \\ =>y=-\sqrt{3}\mathrm{or}y=\sqrt{3} \end{gathered}$$
Therefore, the solution of the given equation is y=$\pm \sqrt{3}$.