Question
Download Solution PDFIf (4x - 7y) = 11 and xy = 8, what is the value of 16x2 + 49y2, given that x and y are positive numbers?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
4x - 7y = 11
xy = 8
Concept used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
4x - 7y = 11
⇒ (4x - 7y)2 = 112
⇒ 16x2 + 49y2 - 56xy = 121
⇒ 16x2 + 49y2 - 448 = 121
⇒ 16x2 + 49y2 = 121 + 448
⇒ 16x2 + 49y2 = 569
∴ The required answer is 569.
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