Question

Plzz solve q.no 22 ,23and 24

Answer 1

1.

x² + 1/x² = 102

x² + 1/x² - 2 = 102 - 2

(x - 1/x)² = 100

X – 1/x = 10

(x - 1/x)³ = x³ - 1/x³ - 3x + 3/x

x³ - 1/x³ = (x – 1/x) (x² + 1/x² + x/x)

x³ - 1/x³ = 10 ( 102+ 1)

x³ - 1/x³ = 1030

2.

X⁴ + 1/x⁴  = 47

(X²  + 1/x²)² = x⁴ + 1/x⁴ + 2

(X² + 1/x²)² = 47 + 2 = 49

X² + 1/x²  = 7

X² + 1/x² + 2 = 7 + 2

(X + 1/x)²  = 9

X + 1/x = 3

(X + 1/x)³ = x³ + 1/x³ + 3x+3/x

27 = x³ + 1/x³ + 3(x + 1/x)

27 = x³ + 1/x³ + 9

x³ + 1/x³  = 27 – 9 = 18

3.

x² + 1/x² = 14

x² + 1/x² + 2 = 14 + 2

(x + 1/x)² = 16

X + 1/x = 4

x3 + 1/x³ = (x+ 1/x) (x2 + 1/x2 - 1

x³ + 1/x³ = (x + 1/x) (x² + 1/x² - 1)

x³ + 1/x³ = 4 ( 14 - 1) = 4(13)

x³ -+ 1/x³ = 52