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

9 years ago

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,

9 years ago

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,