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

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Answer 1 · 2016-07-07T01:33:00

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

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

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

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

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

$m = \frac{- 15 \pm \sqrt{15^{2} - (4 \times 3 \times - 40)}}{2 \times 3}$ $m = (-15 +- sqrt(15^2 - (4 xx 3 xx -40)))/(2 xx 3)$

$m = \frac{- 15 \pm \sqrt{705}}{6}$ $m = (-15 +- sqrt(705))/6$

$l = \frac{10}{\frac{- 15 \pm \sqrt{705}}{6}}$ $l = 10/((-15 +- sqrt(705))/6)$

$l = \frac{60}{- 15 \pm \sqrt{705}}$ $l = 60/(-15 +- sqrt(705))$

Now, we can do our calculation:

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

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

Hopefully this helps!

If 4l−3m=154l - 3m = 15 and lm = 10, then find the value of 16l2+9m216l^2 + 9m^2?