Question

If xm.yn =7889, where x and y are prime numbers , the value of x+y is?​

Answer 1

Given :  $x^m \cdot y^n=7889$

x and y are prime numbers

To Find :  the value of x+y

Solution:

$x^m \cdot y^n=7889$

               7889

    7         1127

    7          161

    7           23

    23           1

7889  = 7 * 7 * 7 * 23

=> 7889  = 7³ * 23¹

7³ * 23¹  = 7889

$x^m \cdot y^n=7889$

on comparing

x = 7  , y = 23

m = 3  , n = 1

Hence x + y = 7 + 23 = 30

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