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  •  Find the number of solutions of  <img alt="2(2(2 a)+2(2 b))=40" src="https://entrancecorner.oncodecogs.com/gif.latex?2%282%282%20a%29&plus;2%282%20b%29%29%3D40"

 Find the number of solutions of  2(2(2 a)+2(2 b))=40  , such that a and b are integer numbers 

Option: 1

33


Option: 2

3


Option: 3

44


Option: 4

6


Answers (1)

best_answer

Given,
2(2(2 a)+2(2 b))=40 and
a and b 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, $a=-(-a), b=-(-b) Then, $[8(a+b)]=40So the equation becomes
a + b = 5
Hence from above equation, n = 5 and r = 2
Hence the total number of solutions =(5+2-1) c_{2-1}=6 c_1=6

Posted by

Ritika Harsh

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