length whose areas are equal to their perimeters. [Hint: The equations x2y that (x 4)(y-4) 8.] 3. For n 3 a given integer, find a Pythagorean triple having n as one of its members. [Hint: For n an odd integer, consider the triple = z and x + y +z xy imply 1 1 (n21) 2 (n 1) п, 2 0129 16E for n even, consider the triple toom Jons ol al 10R (D OLB S (n, (n2/4) - 1, (n2/4) + 1).] do8 Dilenál ozs pb 03 oorlw 4. Verify that (3, 4, 5) is the only Pythagorean triple involving consecutive positive integers. [Hint: Consider the Pythagorean triple (x, x + 1, x +2) and show that x = 3.] mo 5. (a) Establish that there are infinitely many Pythagorean triples (x, y, z) in which x and y are consecutive integers. [Hint: If (x, x + 1, z) happens to be a Pythagorean triple, so is (3x +2z + 1, 3x + 2z + 2, 4x + 3z + 2).] (b) Find five Pythagorean triples of the form (x, x1, z).
length whose areas are equal to their perimeters. [Hint: The equations x2y that (x 4)(y-4) 8.] 3. For n 3 a given integer, find a Pythagorean triple having n as one of its members. [Hint: For n an odd integer, consider the triple = z and x + y +z xy imply 1 1 (n21) 2 (n 1) п, 2 0129 16E for n even, consider the triple toom Jons ol al 10R (D OLB S (n, (n2/4) - 1, (n2/4) + 1).] do8 Dilenál ozs pb 03 oorlw 4. Verify that (3, 4, 5) is the only Pythagorean triple involving consecutive positive integers. [Hint: Consider the Pythagorean triple (x, x + 1, x +2) and show that x = 3.] mo 5. (a) Establish that there are infinitely many Pythagorean triples (x, y, z) in which x and y are consecutive integers. [Hint: If (x, x + 1, z) happens to be a Pythagorean triple, so is (3x +2z + 1, 3x + 2z + 2, 4x + 3z + 2).] (b) Find five Pythagorean triples of the form (x, x1, z).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 4 please
![length
whose areas are equal to their perimeters. [Hint: The
equations x2y
that (x 4)(y-4) 8.]
3. For n 3 a given integer, find a Pythagorean triple
having n as one of its members. [Hint: For n an odd
integer, consider the triple
= z and x + y +z xy imply
1
1
(n21)
2
(n 1)
п,
2
0129 16E
for n even, consider the triple toom
Jons ol al
10R
(D
OLB S (n, (n2/4) - 1, (n2/4) + 1).]
do8 Dilenál
ozs pb
03
oorlw
4. Verify that (3, 4, 5) is the only Pythagorean triple
involving consecutive positive integers. [Hint:
Consider the Pythagorean triple (x, x + 1, x +2) and
show that x =
3.]
mo
5.
(a) Establish that there are infinitely many
Pythagorean triples (x, y, z) in which x and y are
consecutive integers. [Hint: If (x, x + 1, z)
happens to be a Pythagorean triple, so is
(3x +2z + 1, 3x + 2z + 2, 4x + 3z + 2).]
(b) Find five Pythagorean triples of the form
(x, x1, z).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc27b03fb-27ff-4129-a29b-052f3c3c0c2f%2F60bf4a39-356d-4674-9b8f-5e94005a58ee%2F24hbcur.jpeg&w=3840&q=75)
Transcribed Image Text:length
whose areas are equal to their perimeters. [Hint: The
equations x2y
that (x 4)(y-4) 8.]
3. For n 3 a given integer, find a Pythagorean triple
having n as one of its members. [Hint: For n an odd
integer, consider the triple
= z and x + y +z xy imply
1
1
(n21)
2
(n 1)
п,
2
0129 16E
for n even, consider the triple toom
Jons ol al
10R
(D
OLB S (n, (n2/4) - 1, (n2/4) + 1).]
do8 Dilenál
ozs pb
03
oorlw
4. Verify that (3, 4, 5) is the only Pythagorean triple
involving consecutive positive integers. [Hint:
Consider the Pythagorean triple (x, x + 1, x +2) and
show that x =
3.]
mo
5.
(a) Establish that there are infinitely many
Pythagorean triples (x, y, z) in which x and y are
consecutive integers. [Hint: If (x, x + 1, z)
happens to be a Pythagorean triple, so is
(3x +2z + 1, 3x + 2z + 2, 4x + 3z + 2).]
(b) Find five Pythagorean triples of the form
(x, x1, z).
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