Question

Solve ax²-9(a+b)x+(2a²+5ab+2b²)=0

Answer 1

Consider, 9x²-9(a+b)x+(2a²+5ab+2b²)=0

First we will take (2a²+5ab+2b²) and factorize it

= 2a²+4ab+ab+2b²

= 2a(a+2b)+b(a+2b)

= (2a+b)(a+2b)

9x² - 9(a + b)x + (2a² + 5ab + 2b²) = 0

9x² - 9(a + b)x + [(2a + b)(a + 2b)] = 0

9x² - 3*3(a + b)x + [(2a + b)(a + 2b)] = 0

9x² - 3(3a + 3b)x + [(2a + b)(a + 2b)] = 0

9x² – 3[(a + 2b) + (2a + b)]x + [(a + 2b)(2a + b)] = 0

9x² – 3(a + 2b)x - 3(2a + b)x + (a + 2b)(2a + b) = 0

3x[3x – (a + 2b)] - (2a + b)[3x - (a +2b)] = 0

[3x – (a + 2b)][3x - (2a + b)] = 0

[3x – (a + 2b)] = 0 or [3x - (2a + b)] = 0

3x = (a + 2b) or 3x = (2a + b)

Hence, x = $\frac{(a+2b)}{3}$ or x = $\frac{(2a+b)}{3}$