If a = 1/ (a – 5), find

If a = 1/ (a – 5), find

(i) a – 1/a

(ii) a + 1/a

(iii) a² – 1/a².

Answer :

It is given that

a = 1/ (a – 5)

We can write it as

a² – 5a – 1 = 0

Now divide each term by a

a – 5 – 1/a = 0

So we get

a – 1/a = 5

(i) a – 1/a = 5

(ii) We know that

(a + 1/a)² = (a – 1/a)² + 4

Substituting the values

(a + 1/a)² = 5² + 4

So we get

(a + 1/a)² = 25 + 4 = 29

a + 1/a = ± √29

(iii) We know that

a² – 1/a² = (a + 1/a) (a – 1/a)

Substituting the values

a² – 1/a² = ± √29 × 5

a² – 1/a² = ± 5√29

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