Question

find the no. of ordered pairs where x is an integer and y is perfect square, such that y=(x-90)^2-4907​

Answer 1

Answer:

(x−y)

2

+x

2

=25

Now, 3

2

+4

2

=5

2

9+16=25

∴There are 2 possibilities:

I.(x−y)

2

=9 and x

2

=16

∴x=±4 and x−y=±3

(i).x−y=3⇒(4,1) and (−4,−7)

(ii).x−y=−3⇒(4,7) and (−4,−1)

II.(x−y)

2

=16 and x

2

=9

∴x=±3 and x−y=±4

(i).x−y=4⇒(3,−1) and (−3,−7)

(ii).x−y=−4⇒(3,7) and (−3,−1)

∴ Different values of y are 1,−1,7,−7

∴4 different values of y occur.