Find the missing x- and y-values and Pythagorean triples using the identity given
A Pythagorean triple consists of three positive integers a, b, and c, that satisfy the equation from the Pythagorean theorem, thus, a² + b² = c², such triple is commonly written (a,b,c).
We are given the equation : (x²-y²)² + (2xy)² = (x²+y²)² since this, we have :
a = (x²-y²)
b = (2xy)
c = (x²+y²)
Question 1)
X Value: 4
Y Value: 3
Pythagorean triples: ?
Now we can replace the values of x and y, to determine a, b and c.
a = (x²-y²) = (4²-3²) = 16-9 = 7
b = (2xy) = (2*4*3) = 24
c = (x²+y²) = (4²+3²) = 16+9 = 25
Answer 1 : Pythagorean triples : (7,24,25)
Question 2)
X Value: 5
Y Value: ?
Pythagorean Triples: (9,40,41)
Now we have a, b, and c, to determine Y
b = (2xy) = 40
Y = 40/2x = 40/2*5 = 40/10 = 4
Answer 2 : Y = 4
Question 3)
X Value: ?
Y Value: 3
Pythagorean Triples: (27,36,45)
Now we have a, b, and c, to determine X
b = (2xy) = 36
X = 36/2y = 36/2*3 = 36/6 = 6
Answer 3 : X = 6
Question 4)
X Value: 7
Y Value: 5
Pythagorean Triples: ?
Now we can replace the values of x and y, to determine a, b and c.
a = (x²-y²) = (7²-5²) = 49-25 = 24
b = (2xy) = (2*7*5) = 70
c = (x²+y²) = (7²+5²) = 49+25 = 74
Answer 4 : Pythagorean triples : (24,70,74)
Hope this helps!
[tex]\textit{\textbf{Spymore}}[/tex]
