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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.
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,
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