Unknown integer.

Algebra Level pending

The product of three consecutive integers is 504. Find the sum of the integers.


The answer is 24.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Saksham Jain
Nov 12, 2017

Factorize 504 7,8,9 Are nos. 24 is answer

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Pham Khanh
Nov 12, 2017

a ( a + 1 ) ( a + 2 ) = 504 a(a+1)(a+2)=504 ⟺ a 3 + 3 a 2 + 2 a = 504 \iff a^3+3a^2+2a=504 ⟺ a 3 + 3 a 2 + 2 a − 504 = 0 \iff a^3+3a^2+2a-504=0 ⟺ a 3 − 7 a 2 + 10 a 2 − 70 a + 72 a − 504 = 0 \iff a^3-7a^2+10a^2-70a+72a-504=0 ⟺ ( a − 7 ) ( a 2 + 10 a + 72 ) = 0 \iff (a-7)(a^2+10a+72)=0 a 2 + 10 a + 72 = ( a + 5 ) 2 + 47 > 0 a^2+10a+72=(a+5)^2+47 >0 so a = 7 a=7 and the sum is 7 + 8 + 9 = 24 7+8+9=\Large \boxed{24}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

x = 7 x = 7 ? Do you mean a = 7 a = 7 ?

Munem Shahriar - 3 years, 7 months ago

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Sorry. Edited

Pham Khanh - 3 years, 6 months ago

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