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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Question : Simplify the given expression. $\frac{(4.2)^{3} - 0.008}{(4.2)^{2} + 0.84 + 0.04}$

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Answer 1

Correct Answer: 2

Solution : Given: $\frac{(381 + 119)^{2} + (381 - 119)^{2}}{(381)^{2} + (119)^{2}}$
Let $a = 381 a n d b = 119$
$\frac{(a + b)^{2} + (a - b)^{2}}{(a)^{2} + (b)^{2}}$
= $\frac{(a^{2} + b^{2} + 2 a b) + (a^{2} + b^{2} - 2 a b)}{a^{2} + b^{2}}$
= $\frac{a^{2} + b^{2} + a^{2} + b^{2}}{a^{2} + b^{2}}$
= $\frac{2 (a^{2} + b^{2})}{a^{2} + b^{2}}$
= $2$
Hence, the correct answer is 2.

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Question : Simplify the given expression. (381+119)2+(381−119)2(381)2+(119)2Option 1: –1Option 2: –2Option 3: 1Option 4: 2

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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