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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

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

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

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

- Thread starter Albert
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- Thread starter
- #1

- Jan 25, 2013

- 1,225

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

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

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

- Mar 31, 2013

- 1,346

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

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

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

- Thread starter
- #3

- Jan 25, 2013

- 1,225

good solution

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