Question

Determine all ordered pairs that satisfy (x - y)² + x² = 25, where x and y are integers and x > or = to zero. The number of different values of "y" that occur is: (A)3 (B) 4 (C) 5 (D) 6​

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.

Step-by-step explanation:

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