If x + 1/x = 11x+1x=11 , then find the value of x^4 + 1/x^4x4+1x4 ?

3 Answers
St.Roller
Jun 9, 2018

x^4+1/x^4 = 14159x4+1x4=14159

Explanation:

As per the question, we have

x+1/x = 11x+1x=11

:.(x+1/x)^2=(11)^2 ... [Squaring both sides]

:.x^2+1/x^2+2(x)(1/x)=121

:.x^2+1/x^2+2(cancelx)(1/cancelx)=121

:.x^2+1/x^2+2=121

:.x^2+1/x^2=121-2=119 ... (i)

Now, back to x+1/x=11

(x+1/x)^4=(11)^4

:.x^4+1/x^4+4(x^3)(1/x)+6(x^2)(1/x^2)+4(x)(1/x^3)=(11)^4

:.x^4+1/x^4+4(x^2)+6+4(1/x^2)=14641

:.x^4+1/x^4+4(x^2)+4(1/x^2)=14641-6

:.x^4+1/x^4+4(x^2+1/x^2)=14635

:.x^4+1/x^4+4(119)=14635 ... [Substituting the value of x^2+1/x^2 from (i)]

:.x^4+1/x^4+476=14635

:.x^4+1/x^4=14635-476

:.x^4+1/x^4=14159

Hence, the answer.

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Sonnhard
Jun 9, 2018

14159

Explanation:

We use that
(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4
so we get
(x+1/x)^4=x^4+1/x^4+4(x^2+1/x^2)=11^4-6
and
x^2+1/x^2=11^2-2
so we get

x^4+1/x^4=11^4-6-4(11^2-2)=14159

P dilip_k
Jun 9, 2018

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

=>x^2+1/x^2=11^2-2=119

Now x^4+1/x^4=(x^2+1/x^2)^2-2*x^2*1/x^2

=>x^4+1/x^4=119^2-2=14159

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