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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Solutions

Chapter
Section
BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

Pythagorean Triples If a , b , c are positive integers such that a 2 + b 2 = c 2 , then ( a , b , c ) is called a Pythagorean triple.

(a) Let m and n be positive integers with m > n . Let a = m 2 n 2 , b = 2 m n and c = m 2 + n 2 . Show that ( a , b , c ) is a Pythagorean triple.

(b) Use part (a) to find the rest of Pythagorean triple in the table.

m n ( a , b , c )
2 1 ( 3 , 4 , 5 )
3 1 ( 8 , 6 , 10 )
3 2
4 1
4 2
4 3
5 1
5 2
5 3
5 4

To determine

(a)

To show:

That (a,b,c) is a Pythagorean triple.

Explanation

Given:

The following relations:

a=m2n2b=2mnc=m2+n2

Approach:

If a,b,c are positive integers such that a2+b2=c2, then (a,b,c) is called a Pythagorean triple.

For a right angle triangle the Pythagorean Theorem is,

a2+b2=c2 ……(1)

Here, a is the perpendicular of the triangle, b is the base of the triangle and c is the hypotenuse.

Calculations:

Substitute m2n2 for a, 2mn for b and m2+n2 for c in equation (1).

To determine

(b)

To find:

The Pythagorean triples.

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