+0  
 
0
33
1
avatar

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673. Find a - b.

 Dec 30, 2022
 #1
avatar+1317 
+2

These are a system of equations. Add the first two equations, and you get 2a^3 (the 3ab^2 cancel each other out) = 1352. a^3 = 676. 

a = cube root of 676.

Plugging back in, we have 676 + 3cbrt(676)b^2 = 679

cbrt(676)b^2 = 1

1/cbrt(676)

b = sqrt(cbrt(676^2)/676) = cbrt(676)/26

a - b = cbrt(676) - cbrt(676) = 25cbrt(676)/26

 Dec 30, 2022

20 Online Users

avatar