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