Question

Solve for x $:9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0$by the quadratic polynomial.

Answer 1

Consider,

$9x^2-9(a+b)x+(2a^2+5ab+3b^2)$

Comparing with $A{x}^2+Bx+C=0$

We get,

$A=9,B=-9(a+b),C=(2a^2+5ab+2b^2)$

Discriminant $=B^2-4AC=9(a-b{)}^2$

Now using quadratic formula-

$x=\frac{-B\pm \sqrt{B^2-4AC}}{2A}\Rightarrow x=\frac{9(a+b)\pm 3(a-b)}{2\times 9}\Rightarrow x=\frac{(3a+3b)\pm (a-b)}{6}$

$\Rightarrow x=\frac{(a+2b)}{3}orx=\frac{(2a+b)}{3}$