Question

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

Answer 1

`l = 10/m`

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

`40/m - 3m = 15`

`40 - 3m^2 = 15m`

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

By the quadratic formula:

`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!