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Most Important Selected Qs for JEE AdvancedMathematicsTrigonometry

If ^4 x 5 + ^4 x 4 = 1 9 , then which of the following is/are TRUE?

Options

  1. A^2 x= 4 5
  2. B^2 x= 4 5
  3. C64 ^6 x + 125 ^6 x =1458
  4. D125 ^6 x + 64 ^6 x =1458

Correct answer

C. 64 ^6 x + 125 ^6 x =1458

Step-by-step solution

We have 9 5 ^4 x+ 9 4 ^4 x=1 9 5 ^4 x+ 9 4 = ^4 x (on divide throughout by ^4 x ) aligned & 9 5 ^4 x+ 9 4 = (1+ ^2 x )^2 & 16 ^4 x-40 ^2 x+25=0 (4 ^2 x-5 )^2=0 aligned ^2 x= 5 4 Now, ^2 x=1+ ^2 x=1+ 5 4 = 9 4 and cosec ^2 x=1+ ^2 x=1+ 4 5 = 9 5 Hence 64 ^6 x+125 cosec ^6 x= (64 729 64 )+ (125 729 125 )=1458

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