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  • Find the number of solutions of <img alt="\left[2^3(m+n+m+n)\right]=16" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cleft%5B2%5E3%28m&plus;n&plus;m&plus;n%29%5Cright%5D%

Find the number of solutions of \left[2^3(m+n+m+n)\right]=16 , such that m , n  are integer numbers

Option: 1

6


Option: 2

-3


Option: 3

2


Option: 4

33


Answers (1)

Given,
\left[2^3(m+n+m+n)\right]=16 and 
m and n are between .......-3,-2,-1,0,1,2,3, ..........
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, $m=-(-m)$ and $n=-(-n) Then, $m+n=1So the equation becomes
m + n = 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

Ramraj Saini

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