Answer: 17, 19, 21 ✔️are the three consecutive odd numbers.
Step-by-step explanation:
Let n an integer number
Three consecutive odd numbers can be expressed as:
(2·n − 1) , (2·n − 1) + 2 , (2·n − 1) + 4
(2·n − 1) , (2·n + 1) , (2·n + 3)
The product of the greater two is: (2·n + 1) x (2·n + 3)
The product of the smaller two is: (2·n − 1) x (2·n + 1)
If we substract the product of the smaller two from the product of the greater two, the result will be 76.
We can express this:
(2·n + 1) x (2·n + 3) - (2·n - 1) x (2·n + 1) = 76
4n² + 6n + 2n + 3 - [4n² + 2n - 2n - 1] = 76
4n² + 8n + 3 - 4n² - 2n + 2n + 1 = 76
8n + 4 = 76
8n = 76 - 4 = 72
n = 72/8 = 9
Now we can substitute the calculated value for n, and the numbers are:
(2·n − 1) , (2·n + 1) , (2·n + 3)
(2·9 − 1) = 17
(2·9 + 1) = 19
(2·9 + 3) = 21
Answer: 17, 19, 21 ✔️are the three consecutive odd numbers.
Check
If we substract the product of the smaller two from the product of the greater two, the result will be 76:
21x19 - 17x19 = 19(21 - 17) = 19 x 4 = 76✔️ checked!
The three consecutive odd numbers such that the product of the smaller two from the product of the greater two, the result will be 76 are 19,21 and 23.
Given-
Let x be the number.
As these number are consecutive odd numbers. thus we can write them as,
[tex]2x-1[/tex]
[tex]2x-1+2=2x+1[/tex]
[tex]2x-1+4=2x+3[/tex] and so on....
Now in the question we have given that if we subtract the product of the smaller two from the product of the greater two, the result will be 76. Thus,
[tex](2x+1)\times(2x+3)-(2x-1)\times(2x+1)=76[/tex]
[tex]4x^2+6x+2x+3-(4x^2+2x-2x-1)=76[/tex]
[tex]4x^2+8x+3-4x^2+1=76[/tex]
[tex]8x+4=76[/tex]
Divide both side by 4.
[tex]2x+1=19[/tex]
[tex]x=\dfrac{19-1}{2}[/tex]
[tex]x=9[/tex]
The value of x is 9. therefore the value of the numbers are,
[tex]2x-1=2\times9-1=19[/tex]
[tex]2x+1=2\times9+1=21[/tex]
[tex]2x+3=2\times9+3=23[/tex]
Hence the three consecutive odd numbers such that the product of the smaller two from the product of the greater two, the result will be 76 are 19,21 and 23.
For more about the consecutive numbers follow the link below-
https://brainly.com/question/864749
