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Algebra Level 1

n ! + 5 = n 3 , n = ? \color{#20A900}n! + 5 = \color{#20A900}n^3, \ \ \ \ \ \ \color{#20A900}n = \ ?


The answer is 5.

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Preetam Kandula by Preetam Kandula , 21, India

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7 solutions

Chew-Seong Cheong
Mar 23, 2015

The solution can be easily found using a spreadsheet. See below:

The command used are as follows:

  • A2: 1
  • B2: =FACT(A2)+5
  • C2: =A2^3
  • D2: =B2=C2

Copy A2:D2 down to A11:D11 by dragging down.

Dn: =Bn=Cn is a logical function, it returns TRUE if Bn=Cn or FALSE if otherwise.

You can format column D to mark the outcome which is TRUE red by using Conditional Formating > Highlight Cells Rules > Equal To... > "TRUE" > OK.

There is only one solution that is n = 5 n=\boxed{5} .

Try it!

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Wow that's a really great way to think about it.

Avi Tarquini - 6 years, 2 months ago
Jacob Jones
Apr 2, 2015

Basically you can do it by a process of trial and error. Logic shows that it has to be quite a low number in order for it to work both ways. 5 fits if you think about all the possibilities starting with 1.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Rama Devi
Apr 22, 2015

5!=120 & 5^3=125 Therefore the answer is 5

1 Helpful 0 Interesting 0 Brilliant 0 Confused

5!=120 & 5^3=125. . . not worth for 100 points. . .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

i wanted to know if there is any other way to solve it...

Preetam Kandula - 6 years, 3 months ago

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There is,divide the whole expression by 5 on both sides of the = sign.You will see that (n-1)! and n^2 are integers and thus 5/n should also be an integer.Check n=1 and n=5.

Adarsh Kumar - 6 years, 2 months ago
Aryan Mehra
Apr 30, 2017

Please do not use spreadshhets or stuff. Simpke logic says that since n factorial must have had a five and five is added to it. So ideally you should check only the multiples of five. The very first guess is correct. Do not use spreadsheet and waste time.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vivek Singh
Mar 24, 2015

N! + 9 = (n+3)^3 Find n ?

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Pragyan Bhatt
Mar 23, 2015

we should use hit and trail method..by this ....when we put n=5 it setisfy the both side

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Anyway,is there a way to factorize this n^3-n!+5?

Frankie Fook - 6 years, 2 months ago

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As general polynomial factoring I think no. But if you argue that n^3-n!=5 and how the left side has a common factor of n, so n is a factor of 5, you get a variation of the work other people have posted above.

Brian Kelly - 6 years, 2 months ago

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