# Equation

• Apr 3rd 2010, 04:05 AM
bhitroofen01
Equation
Hi people,

I don't know how to calculate $(\sqrt[3]{x}-1)^3-54=0$???

• Apr 3rd 2010, 04:16 AM
earboth
Quote:

Originally Posted by bhitroofen01
Hi people,

I don't know how to calculate $(\sqrt[3]{x}-1)^3-54=0$???

Transfer all terms to the RHS except x:

$(\sqrt[3]{x}-1)^3-54=0$

$(\sqrt[3]{x}-1)^3=54$ Now calculate the 3rd root of both sides of the equation:

$\sqrt[3]{x}-1=\sqrt[3]{54}=3\sqrt[3]{2}$

$\sqrt[3]{x}=1+3\sqrt[3]{2}$ Now get rid of the cube root:

$x=(1+3\sqrt[3]{2})^3$
• Apr 3rd 2010, 04:18 AM
Prove It
Quote:

Originally Posted by bhitroofen01
Hi people,

I don't know how to calculate $(\sqrt[3]{x}-1)^3-54=0$???

$(\sqrt[3]{x} - 1)^3 - 54 = 0$

$(\sqrt[3]{x} - 1)^3 = 54$

$\sqrt[3]{x} - 1 = \sqrt[3]{54}$

$\sqrt[3]{x} - 1 = \sqrt[3]{27\cdot 2}$

$\sqrt[3]{x} - 1 = \sqrt[3]{27} \cdot \sqrt[3]{2}$

$\sqrt[3]{x} - 1 = 3\sqrt[3]{2}$

$\sqrt[3]{x} = 3\sqrt[3]{2} + 1$

$x = (3\sqrt[3]{2} + 1)^3$.