Question

a^2m-5*b^3n-2*c^4p-1=abc where a b c are natural numbers , find the value of 1/mnp pls answer this question ​

Answer 1

Given :  $a^{2m-1}.b^{3n-2}.c^{4p-1} = abc$   , a^2m-5*b^3n-2*c^4p-1=abc  

To find :  value of 1/mnp

Solution:

a^2m-5*b^3n-2*c^4p-1=abc

$a^{2m-1}.b^{3n-2}.c^{4p-1} = abc$

abc = a¹b¹c¹

assuming a, b & c are coprime

Hence Equating power of a with a , b with b c with c

2m - 5 = 1  => 2m = 6 => m = 3

3n - 2 = 1 => 3n = 3 =>  n = 1

4p - 1 = 1 => 4p = 2 => p = 1/2

mnp = (3)(1)(1/2)  =  3/2

1/mnp  = 1/(3/2) = 2/3

1/mnp = 2/3

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