Question : If $2 x+5 y=15$ and $x y=6$, then the value of $4 x^2+25 y^2$ is:
Option 1: 105
Option 2: 95
Option 3: 100
Option 4: 90
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Correct Answer: 105
Solution :
Given, $2 x+5 y=15$ and $x y=6$
Consider, $2x+5y=15$
Squaring both sides, we get,
⇒ $(2x+5y)^2=15^2$
⇒ $4x^2 + 25y^2 + 20xy = 225$
⇒ $4x^2+25y^2+20×(6)=225$
⇒ $4x^2+25y^2=225-120$
⇒ $4x^2+25y^2 = 105$
Hence, the correct answer is 105.
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