Question

ПОМОГИТЕ СРОЧНО !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
ДОКАЗАТЬ ЧТО x^3+1x^3=a(a^2-3) если х+1/x=a

Answer 1

$frac{x+1}{x}=a; ; to ; ; x+1=ax; ,; ; x(a-1)=1; ,; ; x= frac{1}{a-1} \\ frac{x^3+1}{x^3} = frac{(x+1)(x^2-x+1)}{x^3} = frac{axcdot (x^2-x+1)}{x^3} = frac{acdot (x^2-x+1)}{x^2} =\\=frac{acdot (frac{1}{(a-1)^2}-frac{1}{a-1}+1)}{(frac{1}{a-1})^2} =frac{acdotfrac{1-(a-1)+(a-1)^2}{(a-1)^2}}{frac{1}{(a-1)^2}} =acdot (1-a+1+a^2-2a+1)=\\=acdot (a^2-3a+3)ne a(a^2-3)\\ili\\ frac{x^3+1}{x^3}= frac{x^3}{x^3} + frac{1}{x^3} =1+frac{1}{frac{1}{(a-1)^3}}=1+(a-1)^3=$

$=1+a^3-3a^2+3a-1=a^3-3a^2+3a=acdot (a^2-3a+3)\\acdot (a^2-3a+3)ne acdot (a^2-3)$