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 Find the number of solutions of  4(4 t+4 u+4 v)=16 * 2 , such that t , u and v are integer numbers

Option: 1

2


Option: 2

6


Option: 3

1


Option: 4

5


Answers (1)

Given,
4\left ( 4t + 4u + 4v \right ) = 16 * 2 and
t , u and v 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, $t=-(-t), u=-(-u)$ and $v=-(-v) Then, $t+u+v=2
So the equation becomes 
t + u + v = 2
Hence from above equation, n = 2 and r = 3
Hence the total number of solutions =(2+3-1) c_{3-1}=4 c_2=6

Posted by

Sumit Saini

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