Find the value!

Algebra Level 3

If x 2 + x + 1 = 0 x^2 + x+ 1 = 0 , find x 1999 + x 2000 x^{1999} + x^{2000} .


The answer is -1.

Aditya Narayan Sharma by Aditya Narayan Sharma , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Amodh Makhija
Jan 30, 2016

As 1+ ω \omega + ω 2 \omega^{2} =0

Here ω \omega = CUBE ROOT OF UNITY

So we can take x= ω \omega

x 1999 + x 2000 x^{1999} + x^{2000} = ω 1999 \omega^{1999} +
ω 2000 \omega^{2000}

= ω \omega + ω 2 \omega^{2}

= − 1 \boxed{-1}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Ya. Nice approach Dude :) . I posted the solution in basic algebra for 7th grade.

Aditya Narayan Sharma - 5 years, 4 months ago

multiply by (x-1) both sides and we get,

x^3 = 1 (x^3)^666 = 1 x^1998 = 1 now, x^1999 + x^2000 =x^1998(x^2+x) =1.(-1) [x^2+x=-1] given =-1 (ans)

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...