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

Question

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

Team Careers360 · Accepted Answer

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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Question : If (4x−7y)=11 and xy=8, what is the value of 16x2+49y2, given that x and y are positive numbers?Option 1: 596Option 2: 484Option 3: 569Option 4: 448

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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