Question

la suma de la raices de la ecuacion: x^2+(x-3)^2=5+8(2-x)

Answer 1

X² + (X - 3)² = 5 + 8(2 - X)

X² + X² - 6X + 9 = 5 + 16 - 8X

2X² - 6X + 9 = 21 - 8X

2X² - 6X + 8X + 9 - 21 = 0

2X² + 2X - 12 = 0

Donde: a = 2; b = 2; c = -12

$X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$X=\frac{-2\pm \sqrt{2^2-4(2)(-12)}}{2(2)}$

$X=\frac{-2\pm \sqrt{4+96}}{4}$

$X=\frac{-2\pm \sqrt{100}}{4}$

$X=\frac{-2\pm \ 10}{4}$

X1 = [-2 + 10]/4 = 8/4 = 2

X1 = 2

X2 = [-2 - 10]/4 = -12/4 = -3

X2 = -3

Raices: 2, - 3

La suma de las raices: 2 + (-3) = 2 - 3 = -1