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If [(a4 - a2 + 1)/(a4 + a2 + 1)] = 1/8, then the value of a + (1/a) is
1. √(23/7)
2. √(25/9)
3. √7
4. √5

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Correct Answer - Option 1 : √(23/7)

Given

[(a4 - a2 + 1)/(a4 + a+ 1)] = 1/8

Concept

Use identity: (a + b)= a2 + 2ab + b2

Calculation

[(a2- 1 + 1/a2]/[(a2+ 1 + 1/a2] = 1/8

⇒ [(a2+ 1/a+ 2) - 1 - 2]/(a2 + 1/a+ 2) + 1 - 2)] = 1/8

⇒ [(a + 1/a)2 - 3]/[(a + 1/a)2 - 1] = 1/8

⇒ 8[(a + 1/a)2 - 3] = 1[(a + 1/a)2 - 1]

⇒ 8(a + 1/a)- 24 = (a + 1/a)2 - 1

⇒ 8(a + 1/a)2 - (a + 1/a)2 = -1 + 24

⇒ (a + 1/a)[8 - 1] = 23

⇒ (a + 1/a)2 = 23/7

⇒ (a + 1/a) = √(23/7)

∴ Value of (a + 1/a) is √(23/7)

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