यदि `a^(2)+a+1=0`, तो `a^(5)+a^(4)+1` का मान क्या होगा?

Options

A. 1
B. 0
C. `a+1`
D. `a^(2)`

Answer

B

Explanation

Given
`implies a^(2)+a+1=0`……………..i
`implies` to find `a^(5)+a^(4)+1=?`
by formula
`a^(3)-b^(3)=(a-b)(a^(2)+b^(2)+ab)`
`implies a^(3)-1=(a-1)(a^(2)+a+1)`
`implies a^(3)-1=(a-1)(a^(2)+a+1)`
`(b=1)`
`implies a^(3)-1=(a-1)xx0`
`implies a^(3)-1=0`
`implies a^(3)=1`
`implies a^(5)+a^(4)+1`
`implies a^(3)xxa^(3)+a^(3)+a+1`
`implies a^(2)xx1+ax1+1`
`implies a^(2)+a+1=0` from equation ............i
`implies` Answer will be 0