a + 1/a = 17/4. Find (a - 1/a)

Given

a + 1/a = 17/4

Squarring on both sides, we get,

(a + 1/a)2 = (17/4)2

On expanding, we get

a2 + 1/a2 + 2 = 289/16

a2 + 1/a2 = (289/16) – 2

We get,

a2 + 1/a2 = 257/16 ———— (1)

Now, take

a – 1/a

Taking square we get,

(a – 1/a)2 = a2 + 1/a2 – 2

Substituting the value of equation (1), we get,

(a – 1/a)2 = (257/16) – 2

(a – 1/a)2 = 225/16

Taking square root on both sides, we get,

(a – 1/a) = 15/4

Hence, the value of (a – 1/a) = 15/4

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