Question : If $a + b = 24$ and $8ab = 256$, then what is the value of $3 a^2+3 b^2?$
Option 1: 1536
Option 2: 1024
Option 3: 512
Option 4: 1636
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Correct Answer: 1536
Solution :
Given,
$a + b = 24$ and $8ab = 256$
⇒ $2ab=\frac{256}{4}=64$
We know, $(a+b)^2=a^2+b^2+2ab$
Consider $a + b = 24$
Squaring both sides,
⇒ $a^2+b^2+2ab=24^2$
⇒ $a^2+b^2+64=576$
⇒ $a^2+b^2=576-64$
⇒ $a^2+b^2=512$
⇒ $3a^2+3b^2=3\times 512$
⇒ $3a^2+3b^2=1536$
Hence, the correct answer is 1536.
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