The required three consecutive numbers are 35, 36, 37
Let the three consecutive numbers as per the questions are x , x+1 , x+2
Since, According to the question, the product of these three consecutive numbers are 46620
Therefore, we can write
x ( x+1 )( x+2 ) = 46620
x([tex]x^{2}[/tex] + 2x + x + 2 ) = 46620
[tex]x^{3}[/tex]+ [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x = 46620
Now, [tex]x^{3}[/tex] + [tex]2x^{2}[/tex] + [tex]x^{2}[/tex] + 2x - 46620 = 0
[tex]x^{3}[/tex] + [tex]3x^{2}[/tex] + 2x - 46620 = 0
After factorization, we get
( x- 35 )( [tex]x^{2}[/tex] + 38x + 1332 ) = 0
x - 35 = 0 Since ( [tex]x^{2}[/tex] + 38x + 1332 ) will always be a positive number
Therefore, x = 35
So, x + 1 = 35 + 1 = 36
x + 2 = 35 + 2 = 37
Therefore, the numbers are 35 , 36 , 37
To know more about the consecutive numbers, visit here:
https://brainly.com/question/864749
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