Answered

Join the IDNLearn.com community and start finding the answers you need today. Join our knowledgeable community to find the answers you need for any topic or issue.

The difference of cubes of two consecutive natural numbers is 1657. Find the numbers.

Sagot :

Naǫidn
x, x+1 - two consecutive natural numbers

[tex](x+1)^3-x^3=1657 \\ x^3+3x^2+3x+1-x^3=1657 \\ 3x^2+3x+1=1657 \\ 3x^2+3x-1656=0 \\ 3x^2+72x-69x-1656=0 \\ 3x(x+24)-69(x+24)=0 \\ (3x-69)(x+24)=0 \\ 3x-69=0 \ \lor \ x+24=0 \\ 3x=69 \ \lor \ x=-24 \\ x=23 \ \lor \ x=-24[/tex]

x must be a natural number, so x=23.

[tex]x=23 \\ x+1=23+1=24[/tex]

The numbers are 23 and 24.
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.