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If x +1/x=-1 then the value of x8 + 2x6 + x4 is... plz explain properly

If x +1/x=-1 then the value of x8 + 2x6 + x4 is... plz explain properly 

Grade:10

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

x^4( x^4 +2 x^2 +1)
x^4 ( -x)*(-x)
x^6

But given is x^2 = -1-x
x^6 = -(1+x)^3
-x^3 -1-3x(1+x)
-x^3 -1 + 3x^3
2x^3 -1
2(-x-x^2) -1
-2x-2x^2 -1
-2x^2 + 2x^2 = 0
Regards
Arun
25750 Points
4 years ago
Dear student
 
it can be written as x^8 + x^6 + x^6 + x^4
 
x^6 (x^2 + 1) + x^4 (x^2 + 1)
 
x^4 ( x^2 + 1) (x^2 + 1)
 = x^4 ( -x) (-x) 
 = x^6

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