If a + 1/a = 12, then find the value of a^2 + 1/a^2.

Question

Accepted Answer

Given: a + 1/a = 12

We are to find: a^2 + 1/a^2

Recall the algebraic identity:
(a + 1/a)^2 = a^2 + 2*(a)*(1/a) + 1/a^2 = a^2 + 2 + 1/a^2

So,
a^2 + 1/a^2 = (a + 1/a)^2 - 2

Substitute the given value:
a^2 + 1/a^2 = (12)^2 - 2 = 144 - 2 = 142

But this is not matching any correct option as marked. Let's double-check:
Wait, the calculation above is correct, but the options indicate 146 as correct. Let's check the identity:
(a + 1/a)^2 = a^2 + 2*(a)*(1/a) + 1/a^2 = a^2 + 2 + 1/a^2
So,
a^2 + 1/a^2 = (a + 1/a)^2 - 2

So,
a^2 + 1/a^2 = 144 - 2 = 142

But the correct answer should be 142, not 146. The correct option is 142.

Therefore, option 3 is correct.

Final Answer: 142

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Answer

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