If x + 1/x = 4, what is the value of x^2 + 1/x^2?

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

abhimahna · Answer

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

Bunuel · Answer

Similar question: if-x-2-1-x-2-4-what-is-the-value-of-x-4-1-x-175113.html

Abhishek009 · Answer

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

BrentGMATPrepNow · Answer

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:  ² = 4²
Rewrite as:    = 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

MathRevolution · Answer

==> x2+(1/x2)=(x+1/x)2-2x(1/x)=42-2=14 Thus the answer is C.
Answer: C

Arsh4MBA · Answer

(x+1/x)^2 = X^2+2+1/x^2;

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

Ans:C

pushkarajnjadhav · Answer

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.

Kudos if it helps.

Salsanousi · Answer

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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KanishkM · Answer

Manipulate the if part as

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

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

= 14

Answer C

Abhishek009 · Answer

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)

MathRevolution · Answer

=>

( 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

bumpbot · Answer

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If x + 1/x = 4, what is the value of x^2 + 1/x^2?

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If x + 1/x = 4, what is the value of x^2 + 1/x^2?

Prep Toolkit

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