Math, asked by rimshawahla, 7 months ago

if a+1/a = 2 then a - 1/a =?!​

Answers

Answered by abhi569
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 anindyaadhikari13
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)
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