The no. of ordered pairs of integers (x,y) for which 9x²-6x + y² = 24 is= ?

Hi Basit,

The given eqn can be written as (3x-1)²+y²=5²,

3²+4²=5² is the only way 25 can be written as sum of sq of two integers.

So either 3x-1 = +/- 3or4

and y = +/- 3or4

Solve the equations, and you can see (-1,3) (-1,-3) are the only pairs of integers satisfying the equation.

So there are two ordered pairs.

Hope that helps.

Best Regards,

Ashwin (IIT Madras).

I liked that but the ans is 3 ordered pairs.

Hi Basit,

Absolutely.... yeah it should be three ordered pairs.

I'd taken only the Phythogorain Triplets....

The most Trivial one, I'd ignored.

If M²+N² = L², then M=0,N=L is also a set....

So 3x-1 = 5 and y=0 is another trivial possibility.

x=2, y=0.... which is the other ordered pair (2,0).

So total of 3 ordered pairs.

Regards,

Ashwin (IIT Madras).