Question

If α and β are the roots of x²+ 5x -1 = 0, then find-

(i) α³+β³ (ii) α²+β²
​

Answer 1

Answer:

Step-by-step explanation:

Comparing x²+ 5x -1 = 0 with ax²+ bx+c = 0, we get

a = 1, b = 5, c = -1

α+β = -b/a = -5/1 = -5

α×β = c/a = -1/1 = -1

(i) α³+β³ = (α+β)³ - 3αβ(α+β)

α³+β³ = (-5)³ - 3 × (-1) × (-5)

α³+β³ = -125 - 15

α³+β³ = -140

(ii) α²+β² = (α+β)² - 2αβ

α²+β² = (-5)² - 2 × (-1)

α²+β² = 25 + 2

α²+β² = 27