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

If $4l-3m=15$ and $lm=10$, then find the value of $16{l}^{2}+9{m}^{2}$?
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Reagan Blair

Step 1
$l=\frac{10}{m}$
$4\left(\frac{10}{m}\right)-3m=15$
$\frac{40}{m}-3m=15$
$40-3{m}^{2}=15m$
$0=3{m}^{2}+15m-40$
$m=\frac{-15±\sqrt{{15}^{2}-\left(4×3×-40\right)}}{2×3}$
$m=\frac{-15±\sqrt{705}}{6}$
$l=\frac{10}{\frac{-15±\sqrt{705}}{6}}$
$l=\frac{60}{-15±\sqrt{705}}$
Now, we can do our calculation:
$16{\left(\frac{60}{-15±\sqrt{705}}\right)}^{2}+9{\left(\frac{-15±\sqrt{705}}{6}\right)}^{2}$
I will leave the rest of the simplification up to you.