Вправи: 829

829. Розкладіть на лінійні множники квадратний тричлен:

1) nx² + (n – 2)x – 2 = n(x – 2n)(x + 1) = (nx – 2)(x + 1);

D = (n – 2)² – 4 • n • (–2) = n² – 4n + 4 + 8n = n² + 4n + 4 = (n + 2)²;

x₁ = -(n-2)-(n+2)22•n = -n+2-(n+2)2n = -n+2-n-22n = -2n2n = –1

x₂ = -n-2+(n+2)22•n = -n+2+(n+2)2n = 42n = 2n.

2) x² + mx – mn – n² = (x – m – n)(x + n).

D = (–m)² – 4 • 1 • (–mn – n²) = m² + 4mn + 4n² = (m + 2n)²

x₁ = m-(m+2n)22•1 = m-(m+2n)2 = m-m-2n2 = –n.

x₂ = m+(m+2n)22•1 = m+m+2n2 = 2m+2n2 = m + n.