Question

Solve for x : 9x² - 6ax + ( a² - b²) = 0 ?

Answer 1

9x2 - 6ax + a2 - b2 = 0
9x2 – 6ax + (a – b)(a + b) = 0
9x2 – 3x(a – b) – 3x(a + b) + (a – b)(a + b) = 0
3x[3x – (a – b)] – (a + b) [3x – (a – b)]  = 0
[3x – (a – b)][3x – (a + b)]  = 0
[3x – (a – b)] = 0 or [3x – (a + b)] = 0
3x = (a – b) or 3x = (a + b)
∴ x = (a – b)/3 or x = (a + b)/3

Answer 2

Here a=9,b=6a,c=(a^2+b^2)
By using quadratic formula
6a+√36a^2-36(a^2+b^2)/18
And
6a-√36a^2-36(a^2+b^2)/18
By solving it further you will get
x=a+b/3
And
x=a-b/3