So it was our maths exam today and my answer was 5,24,26. I still dont know the real answer.. can someone solve this?
Pythagorean triplet whose smallest member is 5.
Write a pythagorean triplet whose smallest member is 5.?
2015-09-26 11:42 am
回答 (9)
2015-09-26 12:01 pm
✔ 最佳答案
Why did you think that? 26^2 - 24^2 = 676 - 576 = 100,
which is not the square of 5,
it's the square of 10.
But once you know that 10, 24, 26 is a Pythagorean triple,
then 5, 12, 13 must also be a Pythagorean triple.
2015-09-26 6:15 pm
It is worth memorizing a few of the primitive Pythagorean Triples.
3-4-5
5-12-13 <--
7-24-25
8-15-17
If you had memorized that, you'd immediately know that 5-12-13 was the answer.
But you can also write an equation and try and find an integer solution.
a² + b² = c²
5² + b² = c²
25 + b² = c²
c² - b² = 25
So you want a pair of perfect squares that have a difference of 25.
Just start with 6² and see if adding 25 will give you another perfect square.
36 + 25 = 61 (nope)
Continue with 7²:
49 + 25 = 74 (nope)
8²:
64 + 25 = 89 (nope)
9²:
81 + 25 = 106 (nope)
10²:
100 + 25 = 125 (nope)
11²:
121 + 25 = 145 (nope)
12²:
144 + 25 = 169 = 13² (yes!)
Answer:
5-12-13
3-4-5
5-12-13 <--
7-24-25
8-15-17
If you had memorized that, you'd immediately know that 5-12-13 was the answer.
But you can also write an equation and try and find an integer solution.
a² + b² = c²
5² + b² = c²
25 + b² = c²
c² - b² = 25
So you want a pair of perfect squares that have a difference of 25.
Just start with 6² and see if adding 25 will give you another perfect square.
36 + 25 = 61 (nope)
Continue with 7²:
49 + 25 = 74 (nope)
8²:
64 + 25 = 89 (nope)
9²:
81 + 25 = 106 (nope)
10²:
100 + 25 = 125 (nope)
11²:
121 + 25 = 145 (nope)
12²:
144 + 25 = 169 = 13² (yes!)
Answer:
5-12-13
2015-09-26 1:55 pm
If n is odd and greater than 2 then n, (n²-1)/2, (n²+1)/2 is a PT
Here we have n=5, so 5, (5²-1)/2, (5²+1)/2 which simplifies to 5, 12, 13
Here we have n=5, so 5, (5²-1)/2, (5²+1)/2 which simplifies to 5, 12, 13
2015-09-26 7:14 pm
5, 12, 13
2015-09-26 12:16 pm
5, 12, 13
2015-09-26 11:08 pm
5, 12, 13.
2015-09-26 3:12 pm
Hello
A Sq + B Sq = C Sq
A=5, B=12 and C=13. (A 5x5 = 25. + B 12x12 = 144, = 169) C = 13x13 = 169
Andy C
A Sq + B Sq = C Sq
A=5, B=12 and C=13. (A 5x5 = 25. + B 12x12 = 144, = 169) C = 13x13 = 169
Andy C
2015-09-27 5:06 am
It looks like you were close but somehow a factor of 2 got into your answer.
If the larger two numbers in a pythagorean triplet are consecutive, then the pythagorean theorem says:
a^2 + b^2 = (b+1)^2
a^2 = 2b + 1
We can find such a triplet starting from any odd number. In this case a = 5.
25 = 2b+1
b = 12
The triplet is 5, 12, 13.
If the larger two numbers in a pythagorean triplet are consecutive, then the pythagorean theorem says:
a^2 + b^2 = (b+1)^2
a^2 = 2b + 1
We can find such a triplet starting from any odd number. In this case a = 5.
25 = 2b+1
b = 12
The triplet is 5, 12, 13.
2015-09-26 11:46 am
5, 12, 13
收錄日期: 2021-04-21 21:40:35
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