Given the following two pair for values x 1 = 5, y 1 = 4 and x 2 = 1, y 2 = 1/2.
calculate the pythagorean triples associated with each pair.
based on the results of the previous activity, for which values x n and y n is this identity valid?

answer:

pythagorean triple of is

and for is

step-by-step explanation:

a pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². such a triple is commonly written (a, b, c) .

for example (3, 4, 5) is a pythagorean triple,

we need to calculate pythagorean triples of given following two pair values:

for

let a = 5 and b = 4

put value of a and b in a² + b² = c² to get pythagorean triple

5² + 4² = c²

25 + 16 = c²

        41 = c²

take root on the side in above expression,

hence, pythagorean triple of is

for

put value of a and b in a² + b² = c² to get pythagorean triple

take root on the side in above expression,

hence, pythagorean triple property is not valid for 

therefore, pythagorean triple property is valid for 

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2