Answer:
A) 4
Step-by-step explanation:
First note that m cannot exceed 10 otherwise 100-m² will be negative and √(100-m²) will not be a real number much less an integer
Enumerate all values of m from 0 through 10, find the square, subtract from 100 and see if the result is a perfect square.- we take the square root and see if it is an integer value. The table below details everything. m and n are integers on in 4 cases m = 0, 6, 8 or 10.
Hence the answer is 4 solutions
m m² 100-m² √(100-m²)
0 0 100 10
1 1 99
2 4 96 9.797958971
3 9 91 9.539392014
4 16 84 9.16515139
5 25 75 8.660254038
6 36 64 8
7 49 51 7.141428429
8 64 36 6
9 81 19 4.358898944
10 100 0 0
