If 4l−3m=15 and lm=10, then find the value of 16l2+9m2?

Step 1 l=10m 4(10m)−3m=15 40m−3m=15 40−3m2=15m 0=3m2+15m−40 By the quadratic formula: m=−15±152−(4×3×−40)2×3 m=−15±7056 l=10−15±7056 l=60−15±705 Now, we can do our calculation: 16(60−15±705)2+9(−15±7056)2 I will leave the rest of the simplification up to you.

"If 4l−3m=15 and lm=10, then find the value..." was answered by our experts

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

ostowatygjt

Answered question

2022-02-04

4 l - 3 m = 15

and

l m = 10

, then find the value of

16 l^{2} + 9 m^{2}

Answer & Explanation

Reagan Blair

Beginner2022-02-05Added 16 answers

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

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