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The no. of ordered pairs of integers (x,y) for which 9x 2 -6x + y 2 = 24 is= ?

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

Grade:12

3 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 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,

Ashwin (IIT Madras).

basit ali
41 Points
10 years ago

I liked that but the ans is 3 ordered pairs.

Ashwin Muralidharan IIT Madras
290 Points
10 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,

Ashwin (IIT Madras).

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