Verified answer

Hola

m x^2 - n x + x^2 + 2 = -x - 1

m x^2 + x^2 - n x + x + 2 + 1 = 0

(m + 1) x^2 - (n - 1) + 3 = 0

suma soluciones

1) (n - 1)/(m + 1) = 2

Producto de soluciones

2) 3/(m + 1) = -6

De 2)

m + 1 = 3/-6

m + 1 = -1/2

m = -(1/2) - 1

m = -3/2

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En 1)

n - 1 = 2 (m + 1) = 2 (-(3/2) + 1) = 2 (-1/2) = -1

n = -1 + 1

n = 0

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Verifiquemos en

m x^2- n x + x^2 + 2 = -x - 1

(-3/2) x^2 - (0) x + x^2 + 2 = - x - 1

(-3/2) x^2 + x^2 + x + 2 + 1 = 0

(-1/2) x^2 + x + 3 = 0

multiplicamos por -2

x^2 - 2 x - 6 = 0

completamos cuadrados

x^2 - 2 x = 6

x^2 - 2 x + 1 = 7

(x - 1)^2 = 7

x - 1 = +/-√7

x1 = 1 - √7

x2 = 1 + √7

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suma

1 - √7 + 1 + √7 = 2

producto

(1 - √7) (1 + √7) = (1)^2 - (√7)^2 = 1 - 7 = -6

Saludos

¿Mx^2 – nx +x^2 +2 = -x-1?

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