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If $a + 1 a = 2 + 3 + 1 2 + 3$ what is the value of $a 2 + 1 a 2 ?$

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answer is C.

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Detailed Solution

Given-

a + 1 a = 2 + 3 + 1 2 + 3

.
To determine the value of

a 2 + 1 a 2

.
We can simplify it as,
Question Image

Squaring on both sides,

a + 1 a 2 = 42 ⇒ a 2 + 1 a 2 + 2 = 16 [∵ (a + b) 2 = a 2 + b 2 + 2 a b] ⇒ a 2 + 1 a 2 = 14

Thus, the value of

a 2 + 1 a 2

is 14.
Hence, option 3 is the correct option.

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