Question : If $(4 x-7 y)=11$ and $x y=8$, what is the value of $16 x^2+49 y^2$, given that $x$ and $y$ are positive numbers?
Option 1: 596
Option 2: 484
Option 3: 569
Option 4: 448
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Correct Answer: 569
Solution :
Given: $(4 x-7 y)=11$ and $x y=8$
Now, $(4 x-7 y)=11$
⇒ $(4 x-7 y)^2=11^2$ [squaring both sides]
⇒ $16 x^2+49 y^2-56xy=121$
⇒ $16 x^2+49 y^2-56(8)=121$
⇒ $16 x^2+49 y^2=569$
Hence, the correct answer is 569.
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