If 4x - 3y = 12 and xy = 5, then find the value of $\frac{16 x^2+9 y^2}{8}$.
Answer & explanation
Correct answer: option 1
We know that,
(a - b)2 = a2 + b2 - 2ab
4x - 3y = 12
= (4x - 3y)2 = 122
= 16x2 + 9y2 - 24xy = 144
= 16x2 + 9y2 - 24 × 5 = 144
= 16x2 + 9y2 - 120 = 144
= 16x2 + 9y2 = 264
$\frac{16 x^2+9 y^2}{8}$ = $\frac{264}{8}$ = 33