Question

найти значение выражения

$3x^2-6x+3$

при $x=frac{3-sqrt{5}}{2}$

Answer 1

3((3-sqrt(5))/2)^2 - 6 ((3-sqrt5)/2) -3=

3((9-6sqrt(5) + 5)/4) - 6 ((3-sqrt5)/2) -3=

((27-18sqrt(5)+5)/4) -((18+6sqrt(5))/2)-3=

(27-18sqrt(5)+15-36-12sqrt(5)-12)/4=

(-3(1+5sqrt(5)))/4 

Answer 2

$3x^2-6x+3=x^2-2x+1=(x-1)^2=(frac{3-sqrt5}2-1)=frac{(1-sqrt5)^2}4=frac{6-2sqrt5}4=frac{3-sqrt5}2$