Question

If X= 3+√8, then find the value of x³-1/x³. please help​

Answer 1

according to me it's 47.921

Answer 2

$\huge\boxed{Answer}$

x = 3 + √8

Then ,

x + 1/x = (3 + √8) + 1/(3 + √8)

= {(3 + √8)² + 1} / (3 + √8)

= {(9 + 8 + 6√8 + 1} / (3 + √8)

= (18 + 6√8) / (3 + √8)

= 6(3 + √8) / (3 + √8)

x + 1/x = 6

then ,

(x - 1/x) = √(x + 1/x)² - 4

= √(6)² - 4

= √32

= 4√2

Now ,

(x - 1/x)³ = 128√2

x³ - 1/x³ - 3(x - 1/x) = 128√2

x³ - 1/x³ - 12√2 = 128√2

x³ - 1/x³ = 140√2