+0  
 
0
8
1
avatar+795 

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

 Jan 22, 2024
 #1
avatar+225 
+1

We recognize that these expressions both contain the terms \({a}^{3}\) and \(a{b}^{2}\), so we can set these as variables, let \(x = {a}^{3}\) and \(y = a{b}^{2}\).

We now turn this into a linear system of equations, \(x+3y=679\) and \(3x-y=615\)

We solve this system of equations, getting \(x, y=\frac{1262}{5}, \frac{711}{5}\)\(\) 

The Solution eventually is very ugly, but it is \(a-b=\sqrt[3]{\frac{1262}{5}}-\sqrt{\frac{\frac{711}{5}}{\sqrt[3]{\frac{1262}{5}}}}\) which is approximately 1.57617067733.

 Feb 8, 2024

3 Online Users

avatar