the difference from 2 square number is 19 find the two square number
Answers
Answer: 181.
Given: a, b natural numbers (positive integers)
Assumed: a not = b; a > b
Given: a^2 - b^2 = 19
a^2 = 19 + b^2
c^2 = 19
Perfect squares (squares of positive integers):
4 9 16 25 36 49 64 81 100
Differences (looking for 19):
differences 2^2 = 4: 0 5 12 21 …
differences 3^2 = 9: 5 0 7 16 27 …
differences 4^2 = 16: 12 7 0 9 20 …
differences 5^2 = 25: 21 16 9 0 11 24 …
differences 6^2 = 36: 32 27 20 11 0 13 28 …
differences 7^2 = 49: 45 40 33 24 13 0 15 32 …
differences 8^2 = 64: 60 55 48 39 28 15 0 17 36 …
differences 9^2 = 81: 77 72 65 56 45 32 17 0 19
a = 10, b = 9
10^2 - 9^2 = 100 - 81 = 19.
10^2 + 9^2 = 100 + 81 = 181.
Right triangle
a^2 = c^2 + b^2
Right triangle a = 10, b = 9, c = 4.3589
Right triangle: a = hypotenuse; b = opposite side from Angle B; c = adjacent side from Angle B (SQR(19)) = 4.3589.
Angle A = 90;
Angle B = arccos(SQR(19)/a).
Angle B = arccos(4.3589/10) = 64.16 degrees
Angle B = arctan(9/4.3589) = 64.16 degrees
Note-googled it
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