Question

Найдите сумму кубов корней уравнения.

2 x2 - 5x +1 =0

Answer 1

x^3+y^3=(x+y)(x^2+y^2-xy)=(x+y)((x+y)^2-3xy)

2x^2-5x+1=0

x^2-5/2x+1/2=0

(x+y)((x+y)^2-3xy)=5/2((5/2)^2-3/2)=95/8

Answer 2

2x² - 5x +1 =0

D = 25 - 8 = 17

x₁ = (5 - √17)/4 = 5/4 - √17 / 4

x₂ = (5 + √17)/4 = 5/4 + √17 /4

Формула:

(а³ + в³) = (а + в)·(а² -ав + в²)

(х₁³ + х₂³) = ( 5/4 - √17 / 4 + 5/4 + √17 /4)·( 25/16 - 5√17/8 + 17/16 - 25/16 - 5√17/16 + +5√17/16 + 17/16 + 25/16 + 5√17/8 + 17/16 ) = (10/4)·(25/16 + 51/16) = 5/2 · 76/16 =

= 5/2 · 19/4 =  95/8 = 11,875

Ответ: х₁³ + х₂³ = 95/8 = 11,875