Question

using quadratic formula solve for x : a²b²x² - (4b⁴ - 3a⁴) x - 12a²b² = 0

Answer 1

a^2b^2x^2- (4b^4 - 3a^4)x -12a^2b^2 = 0

⇒ a^2 b^2 x^2- 4b^4 x + 3a^4 x -12 a^2 b^2 = 0

taking xb^2 (first term below)and 3a^2(second term below) outside,

⇒ b^2x(a^2 x - 4b^2) + 3a^2(a^2x - 4b^2) = 0

⇒ (a^2 x - 4b^2)(b^2 x + 3a^2) = 0

⇒ (a^2 x - 4b^2) = 0 or (b^2 x + 3a^2) = 0

⇒ a^2 x = 4b^2 or b^2 x = - 3a^2

⇒ x = 4(b^2)/(a^2) or x = - 3*(a^2)/(b^2)

hope it helps