Is it so small?

Algebra Level 4

$\large (x+1)^3 + (x+2)^3 + (x+3)^3 + (x+4)^3 =(x+10)^3$

Find the least rational solution to the equation above.

1 solution

Anish Harsha
Nov 4, 2015

Let's take $x = t+10$ .

If we substitute it in the equation, we reduce our equation to
$3t(t^2 + 40t +230) = 0$

Since the equation $t^2+40t-230 = 0$ has no rational solutions, we must have $t=0$ .

Thus, our equation has only one and least solution in positive integers namely $x=10$ .

So, the only solution is $10$ .

@Anish Harsha The R.H.S term should be $(x+10)^{3}$ not $(x+5)^{3}$ .

A Former Brilliant Member - 5 years, 7 months ago

I've Edited .

Anish Harsha - 5 years, 7 months ago