Question

in a particular base 40 and 43 product is 2350 , what is the sum of them in same base?

Answer 1

(40)₇ + (43)₇ = (113)₇  if in a particular base 40 and 43 product is 2350 ,

Step-by-step explanation:

Let say base is  a

(40)ₐ * (43)ₐ  = (2350)ₐ

=> (4a + 0)  * (4a + 3)  =  2a³ + 3a² + 5a + 0

=> 16a² + 12a  =    2a³ + 3a² + 5a

=>   2a³ - 13a² - 7a = 0

=> 2a² - 13a - 7 = 0

=> 2a² - 14a + a - 7 = 0

=> 2a(a - 7) + 1(a - 7) = 0

=> (2a + 1)(a - 7) = 0

a = 7

(40)ₐ + (43)ₐ =  (4a + 0) + (4a + 3) = 8a + 3  

using a = 7  

8a + 3 = 59

     59

7      8      3

7       1       1

7        0     1

  59   =  (113)₇

 

sum of  40 & 43 in base 7 = 113 in base 7

(40)₇ + (43)₇ = (113)₇

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