Question

Solve for x:
6x^2-6(a+b)x+(4/3a^2+10/3ab+4/3b^2)=0​

Answer 1

6x² - 6(a + b)x + (4/3a² + 10/3ab + 4/3b²)

= 6x² - 6(a + b)x + 1/3*[4a² + 10ab + 4b²]

= 6x² - 6(a + b)x + 1/3*[4a² + 8ab + 2ab + 4b²]

= 6x² - 6(a + b)x + 1/3*[4a(a + 2b) + 2b(a + 2b)]

= 6x² - 6(a + b)x + 1/3*[(a + 2b)(4a + 2b)]

= 6x² - 6(a + b)x + 2/3*[(a + 2b)(2a + b)]

W can write a + b = (a + 2b)/3 + (2a + b)/3

= 6x² - 6[(a + 2b)/3 + (2a + b)/3]x + 2/3*[(a + 2b)(2a + b)]

= 6x(x - (a + 2b)/3) - 6*(2a + b)/3(x - (a + 2b)/3 )

= (6x - 6*(2a + b)/3)*(x - (a + 2b)/3)

= 6(x - (a + 2b)/3)*(x - (2a + b)/3)

Hope, it helps