Question

a+1/a=6 and a#0 find a-1/a, a2-1/a2​

Answer 1

Solution:

See the attachment for solution.

Here,

→ a + 1/a = 6

On squaring, we get,

→ a² + 1/a² + 2 = 36

On subtracting 4, we get,

→ a² + 1/a² - 2 = 32

Now, it is in the form (a - b)², from here, we can easily find out the value of a - 1/a. Then using identity a² - b² = (a + b)(a - b), we can find out the value of a² - 1/a².

Concept Used: Algebraic Identities.

Identity Used:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)

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