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If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ?
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05 Jun 2022, 14:19
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
A. 12
B. 14
C. 16
D. 18
E. 20
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If a + 1/a = 4 then what is the value of a^2 + 1/a^2 ?
[#permalink]
05 Jun 2022, 16:38
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
A. 12
B. 14
C. 16
D. 18
E. 20
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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
gmatclubot
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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