I need help with this question:$\displaystyle 5/2 = 6/(x+4)^2$ (Rationalize the denominator) Thanks
$\displaystyle 5(x+4)^2=12$
$\displaystyle 5(x+4)(x+4)=12$
$\displaystyle 5(x^2+8x+16)=12$
$\displaystyle 5x^2+40x+68=0$
Now you can either sub these values into the quadratic formula or complete the square to find the values of x.
Do you know how to do this?
I'd make sure to rationalise the denominator...
$\displaystyle 5(x + 4)^2 = 12$
$\displaystyle (x + 4)^2 = \frac{12}{5}$
$\displaystyle x + 4 = \pm\sqrt{\frac{12}{5}}$
$\displaystyle x + 4 = \pm \frac{\sqrt{12}}{\sqrt{5}}$
$\displaystyle x + 4 = \pm \frac{2\sqrt{3}}{\sqrt{5}}$
$\displaystyle x + 4 = \pm \frac{2\sqrt{15}}{5}$
$\displaystyle x = -4 \pm \frac{2\sqrt{15}}{5}$
$\displaystyle x = \frac{-20 \pm \sqrt{15}}{5}$.
This should be the same answer you get if you use the Quadratic Formula...