Question

plz answer with brief explanation​

Answer 1

QUESTION:

If x - 1/x = 3, then find the value of x³ - 1/x³.

ANSWER:

• The value of x³ - 1/x³ = 36

GIVEN:

• x - 1/x = 3.

TO FIND:

• The value of x³ - 1/x³.

EXPLANATION:

$\pink{ \bigstar{\boxed{ \bold{\gray{A^3 - B^3 =(A - B)(A^2 + AB + B^2) }}}}}$

$\blue{\bigstar{\boxed{ \bold{\gray{A^2 + B^2 = (A-B)^2 +2AB }}}}}$

A³ - B³ =(A - B)((A-B)² +2AB+AB)

$\red{\bigstar{\boxed{ \bold{\gray{A^3 - B^3 =(A - B)((A-B)^2 +3AB) }}}}}$

x³ - 1/x³ = (x - 1/x)((x - 1/x)² + 3x × 1/x)

Substitute x - 1/x = 3

x³ - 1/x³ = (3)((3)² + 3)

x³ - 1/x³ = (3)(9 + 3)

x³ - 1/x³ = 3 × 12

x³ - 1/x³ = 36

•°• The value of x³ - 1/x³ = 36.