Question

solve for x: 9x²-6ax-(a²-b²)using quadratic formula

Answer 1

Dear Student,

9x² - 6ax - (a² - b²) = 0

Comparing it with Ax² + Bx + C = 0

we get A = 9 , B = -6a , C = - (a² - b²)

x = $\frac{-\mathrm{B}\pm \sqrt{{\mathrm{B}}^2-4\mathrm{AC}}}{2\mathrm{A}}$
x = $\frac{-\left(-6a\right)\pm \sqrt{{\left(-6a\right)}^2-4\left(9\right)\left(-\left(a^2-b^2\right)\right)}}{2\left(9\right)}$
x = $\frac{6a\pm \sqrt{36a^2+36\left(a^2-b^2\right)}}{18}$
x = $\frac{6a\pm 6\sqrt{2a^2-b^2}}{18}$
x = $\frac{a\pm \sqrt{2a^2-b^2}}{3}$
Regards