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505-555 (Easy)|   Algebra|      
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? Updated on: 24 Feb 2024, 10:52
Originally posted by MathRevolution on 24 Sep 2016, 22:46.
Last edited by Bunuel on 24 Feb 2024, 10:52, edited 3 times in total.
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C
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77% (01:08) correct 23% (02:12) wrong based on 607 sessions

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If \(x + \frac{1}{x} = 4\), what is the value of \(x^2 + \frac{1}{x^2}\)?

A. 10
B. 12
C. 14
D. 16
E. 18­
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C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Sep 2016, 23:09
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MathRevolution
(ex 12) (equation) If x+(1/x)=4, \(x^2+(1/x^2)\)=?
A. 10 B. 12 C. 14 D. 16 E. 18
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x + 1/x = 4

Squaring both sides,

\((x + 1/x )^2 = 4^2\)

or \(x^2+(1/x^2) + 2 = 16\)

or \(x^2+(1/x^2) = 14\)

Hence, C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 25 Sep 2016, 02:49
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MathRevolution
If x+(1/x)=4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18
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Similar question: if-x-2-1-x-2-4-what-is-the-value-of-x-4-1-x-175113.html
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 25 Sep 2016, 07:59
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MathRevolution
If \(x+\frac{1}{x}\) =4, \(x^2+\frac{1}{x^2}\)= ?

A. 10
B. 12
C. 14
D. 16
E. 18
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\(x+\frac{1}{x}\) =4

\((x+\frac{1}{x})^2\) = \(4^2\) { Squaring both sides }

Or, \(x^2\) + \(2*x*\frac{1}{x}\)+ \(\frac{1}{x^2}\) = \(16\)

Or, \(x^2\) + \(2\) + \(\frac{1}{x^2}\) = 16

Or, \(x^2+\frac{1}{x^2}\) = \(16 - 2\)

Or, \(x^2+\frac{1}{x^2}\) = \(14\)

So, Answer will be C. 14
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? Updated on: 25 May 2020, 12:53
Originally posted by BrentGMATPrepNow on 25 Sep 2016, 08:27.
Last edited by BrentGMATPrepNow on 25 May 2020, 12:53, edited 1 time in total.
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If x + (1/x) = 4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18
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Given: x + (1/x) = 4

NOTE: since there are squared terms in the expression we're trying to evaluate, we should consider squaring both sides.

Square both sides: [x + (1/x)]² = 4²
Rewrite as: [x + (1/x)][x + (1/x)] = 16
Use FOIL method to expand: x² + 1 + 1 + 1/x² = 16
Simplify: x² + 2 + 1/x² = 16
Subtract 2 from both sides: x² + 1/x² = 14

Answer: C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 27 Sep 2016, 09:07
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==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C.
Answer: C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 17 Sep 2017, 07:58
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MathRevolution
If x+(1/x)=4, \(x^2+(1/x^2)\)=?

A. 10
B. 12
C. 14
D. 16
E. 18
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(x+1/x)^2 = X^2+2+1/x^2;

So x^2+1/x^2 = 16- 2 = 14;

Ans:C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 26 Sep 2017, 23:08
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x + 1/x = 4

Squaring both sides,

(x+1/x)^2 = 4^2

x^2+(1/x^2)+2*x*1/x=16
x^2+(1/x^2)+2=16
x^2+(1/x^2)=14
Hence Answer is option C.

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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 13 Oct 2018, 02:20
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X + 1/x = 4

(x + 1/x)^2 = 4^2

x^2 + 2 (x * 1/x) + 1/x^2 = 16

x^2 + 2 + 1/x^2 = 16

x^2 + 1/x^2 = 16 - 2 = 14

ArjunJag1328 check the above it may clarify your question.

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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Jan 2019, 06:45
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MathRevolution
[Math Revolution GMAT math practice question]

If \(x+(\frac{1}{x})=4\), what is the value of \(x^2+(\frac{1}{x^2})?\)

\(A. 10\)
\(B. 12\)
\(C. 14\)
\(D. 16\)
\(E. 18\)
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Manipulate the if part as

\(x+(\frac{1}{x})^2=16\)

x^2 + 1/x^2 = 16 - 2

= 14

Answer C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 24 Jan 2019, 08:03
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MathRevolution
[Math Revolution GMAT math practice question]

If \(x+(\frac{1}{x})=4\), what is the value of \(x^2+(\frac{1}{x^2})?\)

\(A. 10\)
\(B. 12\)
\(C. 14\)
\(D. 16\)
\(E. 18\)
Show more

\(x+(\frac{1}{x})=4\)

Squaring both sides we have -

\(x^2 + 2*x*\frac{1}{x} + \frac{1}{x^2} = 16\)

Or, \(x^2 + 2+ \frac{1}{x^2} = 16\)

Or, \(x^2 +\frac{1}{x^2} = 14\), Thus Answer must be (C)
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 27 Jan 2019, 18:26
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=>

\(( x + \frac{1}{x} )^2 = x^2 + 2x(\frac{1}{x}) + (\frac{1}{x})^2 = x^2 + (\frac{1}{x})^2 + 2 = 4^2 = 16.\)
Thus, \(x^2 + (\frac{1}{x})^2 = ( x + \frac{1}{x} )^2 - 2 = 16 - 2 = 14.\)

Therefore, the answer is C.
Answer: C
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If x + 1/x = 4, what is the value of x^2 + 1/x^2? 16 May 2026, 04:12
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