Question

if a - 1/a = 4, then what is a squre + 1/a square​

Answer 1

Given

if a - 1/a = 4, then find the value of a² + 1/a²

To find

Value of a² + 1/a²

Solution

According to the question

=> a - 1/a = 4

Squaring both side

=> (a - 1/a)² = (4)²

Applying identity → (a-b)² = a² + b² - 2ab

=> a² + 1/a² + 2 × a × 1/a = 16

=> a² + 1/a² + 2 = 16

=> a² + 1/a² = 16 - 2

=> a² + 1/a² = 14

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)