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

Guest Jan 6, 2023

#1**0 **

**Alright, the first step is very simple**

**So basically subtract 6ab^2 from the first equation and you will get the second equation so 6ab^2 = 6**

**\(6ab^2 = 6\)**

**\(ab^2 = 1\)**

**now, you are asking for a - b**

**\(b^2 = 1/a\)**

**\(\cdot 1/b\) on both sides**

**\(b = 1/ab\)**

**im just doing every possible thing i can do bc this is my first time seeing this so im doing it as well as you sorry**

**\(ab = 1/b\) ok that might be useful**

**oh......**

**\(a^3 + 3 = 679\)**

**\(a^3 = 676\)**

**\(a \approx 8.77639\)**

**so b is 1/ whatever that is. Square rooted.....**

**its approximately 8.43883.... probably not correct, looking at the numbers. Maybe its like the square root of something?**

its like \(\sqrt{71.212}\) not exacly but close

Imcool Jan 6, 2023