TS Police SI Prelims 2022 · Question 49

Question 49 of the TSLPRB SI Preliminary Written Test 2022 (7 August 2022). Try it first, then open the answer and explanation.

1. SI Prelims 2022 · Q49 · Arithmetic · Numbers & Simplification

   If x is an integer satisfying the equation 9x^(2/3) + 9x^(-2/3) = 82 then √(12 + 2√x) =

   1. 1 + √11
   2. 3 + √3
   3. √3 + √5
   4. 2 + √8

   x అనేది 9x^(2/3) + 9x^(-2/3) = 82 అనే సమీకరణాన్ని తృప్తి పరిచే ఒక పూర్ణసంఖ్య అయితే √(12 + 2√x) =

   1. 1 + √11
   2. 3 + √3
   3. √3 + √5
   4. 2 + √8
   Show answer

   Answer: (2) 3 + √3

   సమాధానం: (2) 3 + √3

   Put t = x^(2/3): 9t + 9/t = 82 gives 9t² - 82t + 9 = 0, so t = 9 or 1/9. Only t = 9 gives an integer (x = ±27), and √x needs x ≥ 0, so x = 27. Then √(12 + 2√27) = √(12 + 6√3) = √((3 + √3)²) = 3 + √3.

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