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If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ?

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Carcass
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If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ? [#permalink] New post   05 Jun 2022, 14:19
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If \(a + \frac{1}{a} = 4\) then what is the value of \(a^2 + \frac{1}{a^2}\) ?

A. 12
B. 14
C. 16
D. 18
E. 20

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B
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GreenlightTestPrep
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Re: If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ? [#permalink] New post   05 Jun 2022, 16:38
Carcass wrote:
If \(a + \frac{1}{a} = 4\) then what is the value of \(a^2 + \frac{1}{a^2}\) ?

A. 12
B. 14
C. 16
D. 18
E. 20


Strategy: When I compare the two given expressions, I recognize that \(a^2\) is the square of \(a\), and \(\frac{1}{a^2}\) is the square of \(\frac{1}{a}\).
So, let's see what happens if we take the given equation, \(a + \frac{1}{a} = 4\), and square both sides.

We get: \((a + \frac{1}{a})^2 = 4^2\)

Use FOIL to expand the left side: \(a^2 + 1 + 1 + \frac{1}{a^2} = 16\)

Simplify: \(a^2 + 2 + \frac{1}{a^2} = 16\)

Subtract \(2\) from both sides of the equation: \(a^2 + \frac{1}{a^2} = 14\)

Answer: B
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Re: If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ? [#permalink]
05 Jun 2022, 16:38
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