Question

X^3+1/x^3=756 then x^4+1/x^4=?

Answer 1

Answer:

x⁴  + 1/x⁴  = 6887

Step-by-step explanation:

Correct Question

x³  - 1/x³   = 756

as we know That  

a³ - b³ = (a - b)³ + 3ab(a - b)

using a = x  & b = 1/x

x³ - 1/x³ = (x  - 1/x)³  + 3x(1/x)(x - 1/x)

let say x - 1/x  = c

=> 756  = c³ + 3c

=> c³ + 3c - 756 = 0

=>(c - 9)(c² + 9c  + 84) = 0

=> c = 9

=> x - 1/x  = 9

Squaring both sides

=> x² + 1/x² - 2 = 81

=> x² + 1/x² = 83

(x³ - 1/x³)(x - 1/x)  = 756 * 9

=> x⁴  + 1/x⁴    - x²  - 1/x² = 756 * 9

=>  x⁴  + 1/x⁴  - (x² + 1/x²) = 6804

=> x⁴  + 1/x⁴  - 83 = 6804

=> x⁴  + 1/x⁴  = 6887

Answer 2

Answer:

x⁴  + 1/x⁴  = 6887

Step-by-step explanation:

Correct Question

x³  - 1/x³   = 756

as we know That  

a³ - b³ = (a - b)³ + 3ab(a - b)

using a = x  & b = 1/x

x³ - 1/x³ = (x  - 1/x)³  + 3x(1/x)(x - 1/x)

let say x - 1/x  = c

=> 756  = c³ + 3c

=> c³ + 3c - 756 = 0

=>(c - 9)(c² + 9c  + 84) = 0

=> c = 9

=> x - 1/x  = 9

Squaring both sides

=> x² + 1/x² - 2 = 81

=> x² + 1/x² = 83

(x³ - 1/x³)(x - 1/x)  = 756 * 9

=> x⁴  + 1/x⁴    - x²  - 1/x² = 756 * 9

=>  x⁴  + 1/x⁴  - (x² + 1/x²) = 6804

=> x⁴  + 1/x⁴  - 83 = 6804

=> x⁴  + 1/x⁴  = 6887