Try this beautiful problem Based on Integer useful for ISI B.Stat Entrance.
The number of integer (positive ,negative or zero)solutions of \(xy-6(x+y)=0\) with \(x\leq y\) is
Integer
Algebra
Divisor
Answer: 10
TOMATO, Problem 72
Challenges and Thrills in Pre College Mathematics
Factorize the given equation
Can you now finish the problem ..........
Find the divisor
can you finish the problem........
Given equation is \(xy-6(x+y)=0\)
\(\Rightarrow xy-6x-6y=0\)
\(\Rightarrow xy-6x-6y+36=36\)
\(\Rightarrow (x-6)(y-6)=3^2 \times 2^2\)
Now the numbers of factpr of \(36=9\) i.e \(\{1,2,3,4,6,9,12,18,36\}\)
Thus we may say that 36 has 9 positive divisors, and 9 negative. and x=0 and y=0 is also a solution
the given condition \(x\leq y\) ,so there are 10 non-negetive solution
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