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

  • 5
  • 10
  • 12
  • 9

Key Concepts


Integer

Algebra

Divisor

Check the Answer


But try the problem first…

Answer: 10

Source
Suggested Reading

TOMATO, Problem 72

Challenges and Thrills in Pre College Mathematics

Try with Hints


First hint

Factorize the given equation

Can you now finish the problem ……….

Second Hint

Find the divisor

can you finish the problem……..

Final Step

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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