Question

hey please solve qiestion 19

Answer 1

Its already given X + 1/X = 2

square both side we get

X²+ 2*X*1/X + 1/X² = 4
ie X²+ 1/X²= 2

taking cube

X³+ 3X²*1/X+3X*1/X²+ 1/X³= 8

X³ + 3X + 3/x + 1/X³ = 8

X³ + 3( X+1/X) + 1/X³ = 8

X³+ 3*2 + 1/X³ = 8

X³+1/X³ = 2

Similarly we can prove 4th power also.

Answer 2

Given Is That X +1/X = 2
Squaring Both Sides,
X^2 +1/X^2 + 2=4
X^2+1/X^2=2
Hence Proved.
Cubing first equation,
X^3+1/X^3+3(X+1/X)=8
X^3+1/X^3+3(2)=8
X^3+1/X^3=2
Hence Proved.
Hope it helped.