Question

if x+1/x=2find the value of 8x³+1/x³​

Answer 1

Answer:

40

Step-by-step explanation:

Given, x +1/2x = 2

Multiplying through by 2x,

2x² + 1 = 4x …………………………………………………………………………………….(1)

Now,

8x³ + 1/x³ = (2x)³ +(1/x)³

(Using the identity a³ + b³ = (a+b) (a² - ab + b²) for a=2x and b=1/x)

= [(2x + 1/x)] [(2x)² - 2x.1/x + (1/x)²]

= [(2x² + 1)/x] [4x² - 2 + 1/x²]

= [(2x² + 1)/x] [(4x⁴ - 2x² + 1)/x²]

= [(2x² + 1)/x] [(2x²)² + 2. 2x².1 + 1² - 6x²)/x²]

= [(2x² + 1)/x] [(2x² + 1)² - 6x²)/x²]

Replacing 2x² + 1 by 4x from (1),

= (4x/x) [(4x)² - 6x²)/x²] = 4(16x² - 6x²)/x²

= 4 (10x²/x²) = 4 . 10 = 40

Hence, the value of 8x³ + 1/x³ = 40

Answer 2

Answer:

2

Step-by-step explanation:

Note: x+1/x, x square+ 1/x square, x cube+ 1/x cube= 2