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AP EAMCET2008MathematicsFunctions

Given that a, b 0,1,2, , 9 with a+b 0 and that (a+ b 10 )^x= ( a 10 + b 100 )^y=1000 . Then, 1 x - 1 y is equal to

Options

  1. A1
  2. B1 2
  3. C1 3
  4. D1 4

Correct answer

C. 1 3

Step-by-step solution

Given that, (a+ b 10 )^x= ( a 10 + b 100 )^y=1000 Let a=0 and b=1 aligned & ( 1 10 )^x= ( 1 100 )^y=1000 & 10^ -x =10^ -2 y =10^3 & x=-3, y=- 3 2 & aligned Now, 1 x - 1 y =- 1 3 + 2 3 = 1 3

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