if a+1/a = 2 then a - 1/a =?!
Answers
Answered by
1
Answer:
0
Step-by-step explanation:
=> a + 1/a = 2
Square on both sides:
=> (a + 1/a)² = 2²
=> (a)² + (1/a)² + 2(a)(1/a) = 4
=> a² + 1/a² + 2 = 4. {2(a)(1/a) = 2(1)=2}
=> a² + 1/a² = 2
Subtract 2 from both sides:
=> a² + 1/a² - 2 = 2 - 2
=> a² + (1/a)² - 2(a)(1/a) = 0 {2=2(a)(1/a)}
=> (a - 1/a)² = 0
=> a - 1/a = 0
Answered by
2
Required Answer:-
Given:
- a + 1/a = 2
To find:
- The value of (a - 1/a)
Answer:
- The value of (a - 1/a) is 0
Solution:
Given that,
➡ a + 1/a = 2
Squaring both sides, we get,
➡ (a + 1/a)² = 2²
➡ a² + 1/a² + 2 × a × 1/a = 4
➡ a² + 1/a² + 2 = 4
➡ a² + 1/a² = 4 - 2
➡ a² + 1/a² = 2
➡ a² + 1/a² - 2 = 0
➡ (a - 1/a)² = 0
➡ (a - 1/a) = √0
➡ a - 1/a = 0
Hence, the value of (a - 1/a) = 0
Identity Used:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
Other Identities:
- a² - b² = (a + b)(a - b)
- (a + b)² = (a - b)² + 4ab
- (a - b)² = (a + b)² - 4ab
- (a + b)³ = a³ + b³ + 3ab(a + b)
- (a - b)³ = a³ - b³ - 3ab(a - b)
Similar questions
Math,
3 months ago
English,
3 months ago
Computer Science,
7 months ago
English,
7 months ago
Social Sciences,
1 year ago
Math,
1 year ago