If (4x - 7y) = 11 and xy = 8, what is the value of 16x2 + 49y2, given that x and y are positive numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 569.
Given:
(4x - 7y) = 11 and xy = 8
Formula used:
(a + b)2 = a2 + b2 + 2ab ---- (1)
Calculations:
Using equation (1), we get
⇒ 112 = 16x2 + 49y2 - 2 × 224
⇒ 16x2 + 49y2 = 448 + 121 = 569