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 Find the number of solutions of [10((a+b)+(b+a))]=40 , such that a and b are integer numbers

Option: 1

6


Option: 2

-3


Option: 3

3


Option: 4

33


Answers (1)

best_answer

Given,
[10((a+b)+(b+a))]=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, $a=a$ and $b=b Then $a+b=2So the equation becomes
a + b = 2
Hence from above equation, n = 2 and r = 2
Hence the total number of solutions =(2+2-1) c_{2-1}=3 c_1=3

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