if a + 1 upon A is equals to 6 and a is not equals to zero find minus one upon a and a square minus one upon
Answers
Given : a + 1/a = 6
To find : a² - 1/a²
Solution:
a + 1/a = 6
Squaring both sides
=> a² + 1/a² + 2a(1/a) = 36
=> a² + 1/a² + 2 = 36
=> a² + 1/a² = 34
=> a² + 1/a² - 2a(1/a) = 34 - 2a(1/a)
=> (a - 1/a)² = 34 - 2
=> (a - 1/a)² = 32
=> a - 1/a = ±4√2
a² - 1/a² = (a + 1/a)(a - 1/a)
= 6 (±4√2)
=> a² - 1/a² = ±24√2
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Given: Value of a + 1 / a = 6, a ≠ 0
To find: Value of a - 1 / a?
Solution:
- Now we have given the value of a + 1 / a = 6
- Squaring both sides, we get:
( a + 1 / a )² = 6²
- Now solving the equation further we get:
a² + 1/a² + 2 = 36
a² + 1/a² = 34
- Now we have :
( a - 1/a )² = a² + 1/a² - 2
= 34 - 2
= 32
a - 1/a = √32 = 4√2
- Now we have:
a² - 1/a² = (a + 1/a)(a - 1/a)
= 6 (4√2)
a² - 1/a² = 24√2
Answer:
So the value of a - 1 / a is 4√2 and a² - 1/a² is 24√2