Question

17 If x-1/x= ✓5, find the values of
(1) x2 +1/x2
(ii) x+1/x
(111) x3+1/x3​

Answer 1

Answer:

1)) x2+1/x2 = 7

2)) x+1/x = 3

3)) x3+1/x3 = 18

Step-by-step explanation:

1))

x - 1/x = √5

(x -1/x)² = (√5)²

x²+1/x² - 2.(x.1/x)= 5

x²+1/x² = 5+2 = 7

2)))

(x+1/x)²= x²+1/x² + 2

(x+1/x)²= 7 + 2 = 9

x+1/x = √9

x+1/x = 3

3)))

x³+1/x³= (x+1/x).(x²+1/x²-x.1/x)

x³+1/x³=(3).(7-1)

x³+1/x³=3×6

x³+1/x³ = 18