Question

If (x+(1/x))=4,the value of (x5+(1/x5)) is:

A. 724 B. 500 C. 752 D. 525

Answer 1

Assuming the question as (x + 1/x) = 4------(A)

Squaring on both the sides we get

x2 +(1/x2) + 2 = 16

⇒ x2 +(1/x2) = 14--------(B)

Now

(x2 +(1/x2))(x + 1/x)=14*4;

(x3+1/x3) + (x + 1/x)=56;

(x3+1/x3) = 56-(x + 1/x) ..... and we (x + 1/x) = 4

Therefore .... (x3+1/x3) = 52------(C)

Multiplying (B) and (C)...we get

(x5+1/x5) + (x+1/x) = 14*52

After solving we get....

(x5+1/x5) = 724.

(x^5+1/x^5)+4=(x^2+1/x^2) (x^3+1/x^3)

now,x^2+1/x^2=(x+1/x)^2 -2 (using a^2+b^2+2ab=(a+b)^2)

=>x^2+1/x^2=4^2-2=14

and

x^3-1/x^3=(x+1/x)(x^2-1+1/x^2)

=>x^3+1/x^3=4 (14-1)=>4*13

putting this in main equation we get,

x^5+1/x^5=(14 * 4 *13)-4=>724

Answer 2

Answer:

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