Question

1. If (x - 1/x) =5. fint the volue of
(x^3-1/x^3)​

Answer 1

TO FIND

(x³ - 1/x³)

GIVEN

(x - 1/x) = 5

cube both side

=> (x - 1/x)³ = (5)³

Applying identity (a-b)³=a³ - b³ - 3ab(a - b)

=> x³ - 1/x³ - 3 × x × 1/x(x - 1/x) = 125

Putting the value of x - 1/x

=> x³ - 1/x³ - 5 = 125

=> x³ - 1/x³ = 125 - 5

=> x³ - 1/x³ = 120

SOME IMPORTANT IDENTITIES

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² - 2ab
• (a+b)³ = a³ + b³ + 3ab(a+b)
• (a-b)³ = a³ - b³ - 3ab(a-b)
• a² - b² = (a+b)(a-b)
• a³ - b³ = (a-b)(a²+ab+b²)
• a³ + b³ = (a+b)(a² -ab +b²)