Integer | ISI-B.stat Entrance(Objective from TOMATO) | Problem 72

Try this beautiful problem Based on Integer useful for ISI B.Stat Entrance.

Integer| ISI B.Stat Entrance | Problem 72

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