Question

Solve the given quadratic equation for x : 9x2 – 9(a + b)x + (2a2 + 5ab + 2b2) = 0.

Answer 1

Consider, 9x2-9(a+b)x+(2a2+5ab+2b2)=0
9x2 - 9(a + b)x + (2a2 + 4ab + ab + 2b2) = 0
9x2 - 9(a + b)x + [2a(a + 2b) + b(a + 2b)] = 0
9x2 - 9(a + b)x + [(a + 2b)(2a + b)] = 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)
x = (a + 2b)/3 or x = (2a + b)/3