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