Question

Find the roots of quadratic equations 9x² - 9(a + b)x + (2a² + 5ab + 2b²) = 0

Answer 1

We write -9(a + b)x = -3(2a + b)x - 3(a + 2b)x as

⇒ x = \(\cfrac{2a+b}3\) or x = \(\cfrac{a+2b}3\)

Hence, \(\cfrac{2a+b}3\) and \(\cfrac{a+2b}3\) are the roots of the given equation.