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AP EAMCET202317 May 2023Evening ShiftMathematicsTrigonometric EquationsActual

If 10 ^4 +15 ^4 =6 , then 16 ^6 +27 ^6 =

Options

  1. A43
  2. B54
  3. C62
  4. D59

Correct answer

C. 62

Step-by-step solution

Given: 10 ^4 +15 ^4 =6 aligned & 10 ( ^4 + ^4 )+5 ^4 =6 & 10 ( ( ^2 + ^2 )^2-2 ^2 ^2 )=6-5 ^4 & 10-20 ^2 ^2 =6-5 ^4 & 4 ^4 -20 ^2 =-5 & 20 ^2 -4 ^4 -5=0 & 20 ^2 -4 (1+ ^2 )^2-5=0 & ^4 -3 ^2 + 9 4 =0 ( ^2 - 3 2 )^2=0 & ^2 = 3 2 then, ^2 = 2 3 aligned Now, 16 ^6 +27 ^6 =16 ( 3 2 )^3+27 ( 2 3 )^3=16 27 8 +27 8 27 =62

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