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Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and roots.

## Equations and roots (B.Stat Objective problems)

The number of ordered pair of integers (x,y) satisfying the equation \(x^{2}+6x+y^{2}=4\) is

- 2
- 4
- 6
- 8

**Key Concepts**

Roots

Integers

Equations

## Check the Answer

But try the problem first…

Answer: 4

Source

Suggested Reading

B.Stat Objective Question 71

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

\(x^{2}+6x+y^{2}=4\) gives \((x+3)^{2}\)=13-\(y^{2}\)

Second Hint

for 1st value positive integer of x, we have 1st and 2nd value of y and for 2nd value negative integer of x we have 3rd and 4th value of y

Final Step

then number of ordered pair is 2+2=4.

## Other useful links

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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