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If the value of 3 36^ +5 18^ 5 36^ -3 18^ is a 5 -b c , where a, b, c are natural numbers and gcd (a, c)=1 , then a+b+c is equal to :

Options

  1. A40
  2. B52
  3. C50
  4. D54

Correct answer

B. 52

Step-by-step solution

aligned & 3( 5 +1) 4 +5 ( 5 -1 4 ) 5 ( 5 +1 4 )-3 ( 5 -1 4 ) = 8 5 -2 2 5 +8 & = 4 5 -1 5 +4 5 -4 5 -4 aligned aligned & = 20-16 5 - 5 +4 -11 & = 17 5 -24 11 a=17, b=27, c=11 & a+b+c=52 aligned

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