Question

determine a soma dos quadrados das raizes da equação 2x²-3x+1=0​

Answer 1

Resposta:

$Soma~~das~~ra\'izes\to\dfrac{-b}{a}$

$Produto~~das~~ra\'izes\to\dfrac{c}{a}$

a = 2

b = -3

c = 1

$x_1^2+x_2^2\to(x_1+x_2)^2\\ \\ (x_1+x_2)^2=x_1^2+2.x_1.x_2+x_2^2\\ \\ (x_1+x_2)^2-2x_1x_2=x_1^2+x_2^2\\ \\ \\ (\dfrac{-b}{a})^2-2.\dfrac{c}{a}=x_1^2+x_2\\ \\ .[\dfrac{-(-3}{2}]^2-2.(\dfrac{1}{2})=x_1^2+x_2^2\\ \\ \\ (\dfrac{3}{2})^2-1=x_1^2+x_2^2\\ \\ \dfrac{9}{4}-1=x_1^2+x_2^2\\ \\ \\ \dfrac{9-4}{4}=x_1^2+x_2^2\\ \\\\ \boxed{ x_1^2+x_2^2=\dfrac{5}{4}}$