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x +1/x=3 then find x^5+1/x^5=? Please give full explanation of this Algeria expressions sum.

Arun
25763 Points
3 years ago
Assuming the question as (x + 1/x) = 3
Squaring on both the sides we get
(x + 1/x)2 = 32
x2 +(1/x2) + 2 = 9
⇒ x2 +(1/x2)  = 7
Now cubing on both the sides we get,
[x2 +(1/x2)]3  = 73
LHs is in the form of (a + b)3 = a3 + b3 + 3ab (a + b)
Hence [x2]3 + [(1/x2)]3 + 3 (x2) × (1/x2)[x2 +(1/x2)]  = 343
⇒ x6 + (1/x6) + 3 × 7 = 343
⇒ x6 + (1/x6) + 21 = 343
∴  x6 + (1/x6)  = 343 − 21 = 322
sahil
142 Points
3 years ago
In this question i think we are asked x^5+1/x^5 Solution:x+1/x=3 so x^2+1/x^2+2=9or x^2+1/x^2=7not (x+1/x)(x^2+1/x^2)=7×3=21so x^3+1/x^3+(x+1/x)=21 or x^3+1/x^3=18Now, (x^2+1/x^2)(x^3+1/x^3)=18×7=136or x^5+1/x^5+(x+1/x)=136Finally x^5+1/x^5=133I tried my best to give the answer in simplest way as possible if you are satisfied please approve.
Martin Raj Kumar
26 Points
2 years ago
X+1/X =3, thefore( x+1/x)^2=x^2+1/x^2+2 =9,so x^+x^2=7 . likewise,x^3+1/x^3=18
Also,(x^2+1/x^2)(x^3+1/x^3)=x^5+1/x^5+x+1/X=
18x7=126.
therefore x^5+1/x^5=126-3=123
the  correct answer is 123.The rest of the steps are correct

Naga Durga Devi Marisetti
15 Points
one year ago
x+1/x=3  (Squaring on both sides)
x^2+1/x^2+2=3^2
x^2+1/x^2=9-2=7
x+1/x=3(cubing on both sides)
x^3+1/x^3+3(x+1/x)=3^3
x^3+1/x^3=27-3(3)
x^3+1/^3=18
(x^2+1/x^2)(x^3+1/x^3)=x^5+1/x^5+1/x+x  (a^m*a^n=a^(m+n))
7*18=x^5+1/^5+(x+1/x)
126-(x+1/x)=x^5+1/x^5
126-3=x^5+1/x^5
So x^5+1/x^5=123
Rishi Sharma
10 months ago
Hello Soham,
The solution of the above problem is attached.
I hope the solution will solve all your doubts.
Thank You,
All the Best for the Exams.
yifs
16 Points
2 months ago
x+1/x=3
(x+1/x)2=(3)2
x2+2+1/(x2)=9
x2+1/(x2)=7
(x2+1/(x2))(x2-1+1/(x2))=(7)(7-1)
x4-x2+2-1/(x2)+1/(x4)=42
(x4-x2+2-1/(x2)+1/(x4))-1=(42)-1
x4-x2+1-1/(x2)+1/(x4)=41
(x+1/x)(x4-x2+1-1/(x2)+1/(x4))=(3)(41)
x5+1/(x5)=123