w

Algebra Level pending

w^5+w^4+1


The answer is 0.

Sujit Kumar by sujit kumar , 20, 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

Sujit Kumar
May 7, 2015

ok from next time

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Archit Boobna
Mar 21, 2015

It should be mentioned that w is the imaginary cube root of unity.

w 3 = 1 a n d w ≠ 1 S o , w 3 − 1 = 0 ( w − 1 ) ( w 2 + w + 1 ) = 0 w − 1 ≠ 0 , s o w 2 + w + 1 = 0 S o w 3 ( w 2 + w + 1 ) = 0 S o w 5 + w 4 + w 3 = 0 S o w 5 + w 4 + 1 = 0 { w }^{ 3 }=1\quad and\quad w\neq 1\\ So,\quad \\ { w }^{ 3 }-1=0\\ \left( w-1 \right) \left( { w }^{ 2 }+w+1 \right) =0\\ w-1\neq 0,\quad so\quad { w }^{ 2 }+w+1=0\\ So\quad { w }^{ 3 }\left( { w }^{ 2 }+w+1 \right) =0\\ So\quad { w }^{ 5 }+{ w }^{ 4 }+{ w }^{ 3 }=0\\ So\quad { w }^{ 5 }+{ w }^{ 4 }+1=0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Sujit Kumar This guy is right, you should let us know what w w stands for, I never knew until I read this solution.

Micah Wood - 6 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...