Question

help me this plssssssss explain the steps​

Answer 1

Step-by-step explanation:

x = 6-√32/2

1/x = 1/6-√32/2 = 2/6-√32

Rationalising (2/6-√32)

= 2/6-√32 × 6+√32/6+√32

= 2(6+√32)/(6)²-(√32)²

= 12+2√32/36-32

= 12+2√32/4

x + 1/x = 6-√32/2 + 12+2√32/4

= 12-2√32/4 + 12+2√32/4

= (12-2√32 + 12+2√32)/4

= 24/4

= 6 (eqn no. i)

(x + 1/x)² = (6)²

x² + (1/x)² + 2 × x × 1/x = 36

x² + 1/x² + 2 = 36

x² + 1/x² = 36-2

x² + 1/x² = 34 (eqn no. ii)

(x + 1/x)³ = (6)³

x³ + 1/x³ + 3 × x × 1/x (x + 1/x) = 216

x³ + 1/x³ + 3 (x + 1/x) = 216

x³ + 1/x³ + 3 (6) = 216

x³ + 1/x³ + 18 = 216

x³ + 1/x³ = 216-18

x³ + 1/x³ = 198 (eqn no. iii)

value of (x³ + 1/x³) - 6 (x² + 1/x²) + (x + 1/x)

(putting values from eqn no. i , ii & iii)

= 198 - 6(34) + 6

= 198 - 204 + 6

= 0