Question : If $(x + 1)^2 + (x + 2)^2 = 16$, then what is the value of $4x^2 + 12x + 40$?
Option 1: 52
Option 2: 62
Option 3: 56
Option 4: 74
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Correct Answer: 62
Solution :
$(x + 1)^2 + (x + 2)^2 = 16$
$⇒x^2+2x+1+x^2+4x+4=16$
$⇒2x^2+6x+5=16$
$⇒2x^2+6x=11$
Adding 20 on both sides, we get,
$⇒2x^2+6x+20=11+20$
Multiplying 2 on both sides, we get,
$⇒2(2x^2+6x+20)=2(31)$
$⇒4x^2 + 12x + 40=62$
Hence, the correct answer is 62.
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