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

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Answer 1 · 2016-07-07T01:33:00

$l = 10/m$

$4(10/m) - 3m = 15$

$40/m - 3m = 15$

$40 - 3m^2 = 15m$

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

$m = (-15 +- sqrt(15^2 - (4 xx 3 xx -40)))/(2 xx 3)$

$m = (-15 +- sqrt(705))/6$

$l = 10/((-15 +- sqrt(705))/6)$

$l = 60/(-15 +- sqrt(705))$

Now, we can do our calculation:

$16(60/(-15 +- sqrt(705)))^2 + 9((-15 +- sqrt(705))/6)^2$

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 16l^2 + 9m^216l^2 + 9m^2?