# find: a³ + b³ + c³

#### Albert

##### Well-known member
$a+b+c+3=2(\sqrt a +\sqrt {b+1}+\sqrt {c-1})$

$find:a^3+b^3+c^3=?$

##### Well-known member
Re: find :a^3+b^3+c^3

$a+b+c+3=2(\sqrt a +\sqrt {b+1}+\sqrt {c-1})$

$find:a^3+b^3+c^3=?$
Let a = $x^2$, b = $y^2-1$, c = $z^2+ 1$
We get $x^2 + y^2 + z^2 + 3 = 2x + 2y + 2z$
Or$(x^2 – 2x + 1) + (y^2 – 2y + 1) + (z^2-2z +1)=0$
Or $(x-1)^2 + (y-1)^2 + (z-1)^2 = 0$
x = y = z = 1 or a = 1, b = 0, c = 2 => $a^3 + b^3 + c^3$ = 9

#### Albert

##### Well-known member
Re: find :a^3+b^3+c^3

Let a = $x^2$, b = $y^2-1$, c = $z^2+ 1$
We get $x^2 + y^2 + z^2 + 3 = 2x + 2y + 2z$
Or$(x^2 – 2x + 1) + (y^2 – 2y + 1) + (z^2-2z +1)=0$
Or $(x-1)^2 + (y-1)^2 + (z-1)^2 = 0$
x = y = z = 1 or a = 1, b = 0, c = 2 => $a^3 + b^3 + c^3$ = 9
good solution