Question : Simplify the given expression. $\frac{(381+119)^2+(381-119)^2}{(381)^2+(119)^2}$
Option 1: –1
Option 2: –2
Option 3: 1
Option 4: 2
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Correct Answer: 2
Solution :
Given: $\frac{(381+119)^2+(381-119)^2}{(381)^2+(119)^2}$
Let $a=381\ and\ b= 119$
$\frac{(a+b)^2+(a-b)^2}{(a)^2+(b)^2}$
= $\frac{(a^2+b^2+2ab)+(a^2+b^2-2ab)}{a^2+b^2}$
= $\frac{a^2+b^2+a^2+b^2}{a^2+b^2}$
= $\frac{2(a^2+b^2)}{a^2+b^2}$
= $2$
Hence, the correct answer is 2.
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