Radical Equation for X

Algebra Level 3

9 + x 3 + 9 x 3 = 3 2 3 \sqrt[3]{9 + \sqrt x} + \sqrt[3]{9-\sqrt x} = 3 \sqrt[3]2

Find the integer x x which satisfies the above equation.


The answer is 49.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Shaun Leong
Feb 15, 2016

Using ( a + b ) 3 = a 3 + b 3 + 3 a b ( a + b ) (a+b)^3=a^3+b^3+3ab(a+b) where a = 9 + x 3 a=\sqrt[3]{9+\sqrt{x}} and b = 9 x 3 b=\sqrt[3]{9-\sqrt{x}} , 9 + x 3 + 9 x 3 = 3 2 3 \sqrt[3]{9+\sqrt{x}}+\sqrt[3]{9-\sqrt{x}}=3\sqrt[3]{2} 18 + 3 ( 3 2 3 ) 81 x 3 = 54 \Rightarrow 18+3(3\sqrt[3]{2})\sqrt[3]{81-x}=54 81 x 3 = 2 4 3 \Rightarrow \sqrt[3]{81-x}=2\sqrt[3]{4} 81 x = 32 \Rightarrow 81-x=32 x = 49 \Rightarrow x=\boxed{49}

Samer Ayoub
Feb 14, 2016

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...