If a² + 1/a² = 102, find the value of a-1/a.
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0
Answer:
10, -10
Step-by-step explanation:
(a-1/a)^2
Expand and substitute.
Answered by
3
Given : a² + 1/a² = 102 …….(1)
To find : The value of a - 1/a.
Solution :
By using an identity : (a – b)² = a² + b² – 2ab
We know that , (a - 1/a)² = a² + 1/a² - 2 × a ×1/a
(a - 1/a)² = a² + 1/a² - 2
(a - 1/a)² = 102 - 2
[From eq 1]
(a - 1/a)² = 100
Taking square root both sides :
a - 1/a = √100
a - 1/a = 10
Hence the value of a -1/a is 10.
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