Question

if a^2m-5.b^3n-2.c^4p-1=abc where a,b,c are natural no.s then 1/MNP equal to. 1) 2/3 ,2) 5/2. 3) 1,. 4) 49/12​

Answer 1

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

To find : Value of  1/MNP

Solution:

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

abc = a¹b¹c¹

Assuming that  a , b & c are co prime

Hence equating power of  a , b & 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

option 1

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