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 Find the number of solutions of [2(2(2(x+y)))]=2^4, such that x and y are even numbers

Option: 1

12


Option: 2

9


Option: 3

2


Option: 4

18


Answers (1)

Given,
[2(2(2(x+y)))]=2^4 and x, y>0
Generalized formula to find the number of solutions of equations is
$$ a_1+a_2+\ldots . .+a_r=(n+r-1) c_{r-1} $$ Let, $x, y>0$ and $y=2 y Then, $x+y=2
So the equation becomes
x + y = 1
Hence from above equation, n = 1 and r = 2 
Hence the total number of solutions =(1+2-1) c_{2-1}=2 c_1=2

Posted by

Sumit Saini

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