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Find all integral solutions (a, b) ∈ Z2 for each of the following three equations:a2+b2=1,a2+b2=2 and a2+b2=9.

Question

Find all integral solutions (a, b) ∈ Z2 for each of the following three equations:

a2+b2=1,a2+b2=2 and a2+b2=9.

 

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Step 1
  1. To find: 
The integral solution for two integers a, b such that a2 +b =1
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The integral solution for two integers a, b such that a2 +b =1

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Step 2

Solution:

The equation is a2+b =
where a,beZ that it represents a circle, thus the possible
1
1
values for a and b can be a
and a = t
1,b 0,a= 0,b =1
1
1
are not integers
However, the values a = t-
Thus, the values of a, and b that satisfy the equation a
a 0, b 1
+b = 1 are
a=1,b 0, and
Hence, the integral solution to the equation a2+b =1 is (1,0),(-1,0). (0,1) and
(0,-1)
_
help_outline

Image Transcriptionclose

The equation is a2+b = where a,beZ that it represents a circle, thus the possible 1 1 values for a and b can be a and a = t 1,b 0,a= 0,b =1 1 1 are not integers However, the values a = t- Thus, the values of a, and b that satisfy the equation a a 0, b 1 +b = 1 are a=1,b 0, and Hence, the integral solution to the equation a2+b =1 is (1,0),(-1,0). (0,1) and (0,-1) _

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Step 3

To find:...

The integral solution for two integers a, b such that a2 +b 2
help_outline

Image Transcriptionclose

The integral solution for two integers a, b such that a2 +b 2

fullscreen

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