If x + 1/x = 2, what is the value of x^9 + 1/X^9 = ?

Question

If  x + \frac{1}{x} = 2 , what is the value of  x^9 + \frac{1}{x^9}  ?

A. -2
B. -1
C. 1
D. 2
E. 4

WarriorWithin · Accepted Answer

It looks difficult to figure out what should be the approach for this question. Looks like there is no equation/ expression which can resolve this -

x + \frac{1}{x} = 2  --> Just look for the values which satisfies the equation - and its definitely 1. No other value except 1 satisfies the equation. This gives us x=1

Put this in the required equation and we get answer as 2, which is option D.

daniformic · Answer

x + \frac{1}{x} = 2, x^9 + \frac{1}{x^9} =?
 1 + \frac{1}{1} = 2, 1 + \frac{1}{1} =2

Ans D

ET10 · Answer

1) Multiplied the first equation by x to get x^2 + 1 = 2x.
2) Subtracted 2x from both sides of the equation to get it into a quadratic equation of x^2 - 2x + 1 = 0
3) Factored the quadratic to get (x-1)^2, so x = 1
4) Plug 1 in for x into the second equation 1^9 + 1/1 = 2. Answer choice D

IMO D

jerryjz2690 · Answer

Factor out x + 1/x =2 by multiplying x on each side.

x^2 + 1 = 2x
x^2 - 2x + 1 = 0
(x-1)^2 = 0
x = 1

1 + 1 = 2

Answer D

CrackverbalGMAT · Answer

Another method would have been using algebraic equations

a^3 + b^3 = (a + b)^3 - 3ab(a + b)

So,  x^3 + \frac{1}{x^3} = (x + \frac{1}{x})^3 - 3 * x * \frac{1}{x}(x + \frac{1}{x}) = (x + \frac{1}{x})^3 - 3(x + \frac{1}{x}) = 2^3 - (3*2) = 2

Now,  x^9 + \frac{1}{x^9} = (x^3 + \frac{1}{x^3})^3 - 3(x^3 + \frac{1}{x^3}) = 2^3 - (3*2) = 8 - 6 = 2

Option D

Arun Kumar

ScottTargetTestPrep · Answer

Solution:
 
Let’s solve the equation by multiplying both sides by x:

x^2 + 1 = 2x

x^2 - 2x + 1 = 0

(x - 1)^2 = 0

x - 1 = 0

x = 1

Since x = 1, x^9 + 1/x^9 = 1 + 1 = 2.

Answer: D

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If x + 1/x = 2, what is the value of x^9 + 1/X^9 = ?

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If x + 1/x = 2, what is the value of x^9 + 1/X^9 = ?

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