Question

Разложить на множители (3а-4)²-(а+7)²

Answer 1

(3a – 4)² – (a + 7)² = (9a² – 24a + 16) – (a² + 14a + 49) = (9 – 1)a² – (24 + 14)a + (16 – 49) = 8a² – 38a – 33

8a² – 38a – 33 = 0

D = 38² + 4·8·33 = 1444 + 1056 = 2500 = 50²

a₁ = (38 – 50) / (2·8) = –12/16 = –3/4 = –0,75

a₂ = (38 + 50) / (2·8) = 88/16 = 11/2 = 5,5

(3a – 4)² – (a + 7)² = 8(a + 0,75)(a – 5,5)