Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Answer:
The 3 numbers are 9, 12, and 15.
Step-by-step explanation:
I will answer in English, below the answer you can see a translation in Catalan.
This can be translated to:
The sum of the squares of three consecutive and multiple natural numbers of 3 is equal to 450. Pose a quadratic equation and calculate the three numbers.
First, a multiple of 3 can be written as:
3*n
The consecutive multiple of 3 is:
3*n + 3
The consecutive multiple of 3 is:
3*n + 3 + 3
Then the sum of their squares is:
(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2
And we know that this is equal to 450, then we need to solve the equation:
(3*n)^2 + (3*n + 3)^2 + (3*n + 6)^2 = 450
let's solve this:
9*n^2 + (9*n^2 + 2*(3*n)*3 + 9) + (9*n^2 + 2*(3*n)*6 + 36) = 450
27*n^2 + 54*n + 45 = 450
we can write this as:
27*n^2 + 54*n + 45 - 450 = 0
27*n^2 + 54*n - 405 = 0
The solutions of this equation are given by the Bhaskara's formula, and the solutions are:
[tex]n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)} }{2*27} = \frac{-54 \pm 216 }{54}[/tex]
we know that our numbers are naturals, then the numbers are positives, which means that we only care for the positive solution of n, which is:
n = (-54 + 216)/54 = 3
Then the 3 numbers are:
3*n = 3*3 = 9
(3*n + 3) = (3*3 + 3) = 12
(3*n + 6) = (3*3 + 6) = 15
In Catalan:
En primer lloc, es pot escriure un múltiple de 3 com:
3 * n
El múltiple consecutiu de 3 és:
3 * n + 3
El múltiple consecutiu de 3 és:
3 * n + 3 + 3
Llavors, la suma dels seus quadrats és:
(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2
I sabem que això és igual a 450, llavors hem de resoldre l’equació:
(3 * n) ^ 2 + (3 * n + 3) ^ 2 + (3 * n + 6) ^ 2 = 450
resolem això:
9 * n ^ 2 + (9 * n ^ 2 + 2 * (3 * n) * 3 + 9) + (9 * n ^ 2 + 2 * (3 * n) * 6 + 36) = 450
27 * n ^ 2 + 54 * n + 45 = 450
podem escriure això com:
27 * n ^ 2 + 54 * n + 45 - 450 = 0
27 * n ^ 2 + 54 * n - 405 = 0
Les solucions d’aquesta equació vénen donades per la fórmula de Bhaskara, i les solucions són:
[tex]n = \frac{-54 \pm \sqrt{54^2 -4*27*(-415)} }{2*27} = \frac{-54 \pm 216 }{54}[/tex]
sabem que els nostres nombres són naturals, aleshores els nombres són positius, cosa que significa que només ens importa la solució positiva de n, que és:
n = (-54 + 216) / 54 = 3
Llavors els 3 nombres són:
3 * n = 3 * 3 = 9
(3 * n + 3) = (3 * 3 + 3) = 12
(3 * n + 6) = (3 * 3 + 6) = 15
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
