Solve the following quadratic equation by formula method 36 y^2-1… - Vidyadip

Question

Solve the following quadratic equation by formula method
$36 y^2-12 a y+\left(a^2-b^2\right)=0$

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Answer

$\begin{aligned} & \text { Here } a=36, b=-12 a, c=a^2-b^2 \\ & x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\ & =\frac{12 a \pm \sqrt{144 a^2-4(36)\left(a^2-b^2\right)}}{2(36)} \\ & =\frac{12 a \pm \sqrt{144 a^2-144 a^2+144 b^2}}{72} \\ & =\frac{12 a \pm \sqrt{144 b^2}}{72} \\ & =\frac{12 a \pm 12 b}{72} \\ & =\frac{12(a \pm b)}{72} \\ & =\frac{(a \pm b)}{6} \\ & =\frac{(a+b)}{6} \text { or } \frac{(a-b)}{6}\end{aligned}$
The solution set is $\frac{( a + b )}{6}$ and $\frac{( a - b )}{6}$

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