Math, asked by ankitkumar0102, 1 year ago

Let a and b be the roots of the equation x2 + x + 1 = 0. The equation whose roots are a19, b7 is:

Answers

Answered by kvnmurty
8
x² + x + 1 = 0  
multiply the equation by  (1 - x) =>  1 - x³ = 0

x is a cube root of 1:  denoted by ω or w² :  as  1 + ω + ω² = 0  or  1 + ω² + ω⁴ = 0

a = ω    and  b = ω²

a¹⁹ =  a¹⁸⁺¹ = (a³)⁶ * a = 1⁶ * a = a = ω
b⁷ = b⁶ * b = (b³)² * b = 1² * b = b = ω²


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