This Cambridge Math Problem Stumped Me (Until I Used This Trick!)

Can you solve this challenging system of equations from a Cambridge entrance exam? This math problem looks impossible at first glance, but once you see the "conjugate cube" trick, the solution becomes incredibly elegant.

In this video, we break down:
How to identify the (a + b)³ = a³ + 3a²b + 3ab² + b³ expansion in complex systems.
Using √2 as a key to unlock the second equation.
Solving a cubic equation using synthetic division.
Verifying the real roots to ensure the solution is correct.

Timestamps:
00:00 - The Problem: A Cambridge Classic
00:21 - Spotting the Cubic Expansion Pattern
00:52 - The √2 Trick
03:41 - Forming the Conjugate Equations
06:05 - Simplifying via Substitution
08:31 - Synthetic Division Breakdown
11:25 - Final Verification & Solution

Can you solve it? Pause the video at the start and try it yourself. Let me know your answer in the comments below!
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Видео This Cambridge Math Problem Stumped Me (Until I Used This Trick!) канала NonsoMaths