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5x2 – 7x + 1 = 0, then the value of (x2 + 1/25x2)
1. 19/25
2. 29/25
3. 39/25
4. 59/25

1 Answer

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Correct Answer - Option 3 : 39/25

Given:

5x2 – 7x + 1 = 0

Formula used:

x2 + 1/x2 = a2 – 2

Calculation:

5x2 – 7x + 1 = 0

⇒ 5x – 7 + 1/x = 0 [Divide both side with1/x]

⇒ 5x + 1/x = 7

⇒ x + 1/5x = 7/5 [Divide both side with 1/5]

⇒ x2 + 1/25x2 + \(2.{\rm{x}}.\frac{1}{{5{\rm{x}}}}\)= 49/25 [Squaring both side]

⇒ x2 + 1/25x2 = 49/25 – 2/5

⇒ x2 + 1/25x2 = (49 – 10)/25

⇒ x2 + 1/25x2 = 39/25

∴ Required answer is 39/25

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