# If 4l - 3m = 15 and lm = 10, then find the value of 16l^2 + 9m^2?

Jul 7, 2016

$l = \frac{10}{m}$

$4 \left(\frac{10}{m}\right) - 3 m = 15$

$\frac{40}{m} - 3 m = 15$

$40 - 3 {m}^{2} = 15 m$

$0 = 3 {m}^{2} + 15 m - 40$

$m = \frac{- 15 \pm \sqrt{{15}^{2} - \left(4 \times 3 \times - 40\right)}}{2 \times 3}$

$m = \frac{- 15 \pm \sqrt{705}}{6}$

$l = \frac{10}{\frac{- 15 \pm \sqrt{705}}{6}}$

$l = \frac{60}{- 15 \pm \sqrt{705}}$

Now, we can do our calculation:

$16 {\left(\frac{60}{- 15 \pm \sqrt{705}}\right)}^{2} + 9 {\left(\frac{- 15 \pm \sqrt{705}}{6}\right)}^{2}$

I will leave the rest of the simplification up to you.

Hopefully this helps!