(i) (a + 1/a)2 + (a – 1/a)2
(ii) (a + 1/a)2 – (a – 1/a)2
Answer :
(i) (a + 1/a)2 + (a – 1/a)2
It can be written as
= [a2 + (1/a)2 + 2 × a × 1/a] + [a2 + (1/a)2 – 2 × a × 1/a]
By further calculation
= [a2 + 1/a2 + 2] + [a2 + 1/a2 – 2]
So we get
= a2 + 1/a2 + 2 + a2 + 1/a2 – 2
= 2a2 + 2/a2
Taking 2 as common
= 2 (a2 + 1/a2)
(ii) (a + 1/a)2 – (a – 1/a)2
It can be written as
= [a2 + (1/a)2 + 2 × a × 1/a] – [a2 + (1/a)2 – 2 × a × 1/a]
By further calculation
= [a2 + 1/a2 + 2] – [a2 + 1/a2 – 2]
So we get
= a2 + 1/a2 + 2 – a2 – 1/a2 + 2
= 4
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