Analytical Geometry> x +1/x=3 then find x^5+1/x^5=? Please giv...

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

Soham Rangnekar , 8 Years ago

Grade 8

6 Answers

Arun

Last Activity: 8 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

Last Activity: 7 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

Last Activity: 7 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

Last Activity: 6 Years 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

Last Activity: 5 Years 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. 645-564_WhatsApp Image 2020-06-06 at 3.43.34 PM.jpeg