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Find the values of $a$ and $b$ , if $2 + 1 2 − 1 − 2 − 1 2 + 1 = a + 2 b$ .

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a = 0, b = 5

a = 0, b = 0

a = 0, b = 4

a = 2, b = 2

answer is C.

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Detailed Solution

Given,

2 + 1 2 − 1 − 2 − 1 2 + 1 = a + 2 b

.
Simplify the given expression.

⇒ 2 + 1 2 − 1 − 2 − 1 2 + 1 = a + 2 b

Solve LHS by taking LCM.

⇒ (2 + 1) 2 − (2 − 1) 2 (2) 2 − (1) 2

⇒ 2 + 1 + 22 − 2 − 1 + 22 2 − 1

⇒ 3 + 22 − 3 + 22 1

⇒ 42

Compare the LHS with RHS.

0 + 42 = a + 2 b

⇒ a = 0 ⇒ b = 4

Hence, the correct option is 3.

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