Can You Solve This High School Math Challenge Algebra Problem?

In this math tutorial, we solve the nonlinear simultaneous system x-√(yz) = 42, y-√(zx) = 6, z-√(xy) = -30 using a sophisticated multi-step strategy that transforms three radical equations into a clean linear system. We substitute x = a², y = b², z = c² to eliminate all radicals and rewrite the system in terms of a, b, and c. We then multiply the first equation by b, the second by c, and the third by a, and add all three to get equation 4. We repeat the process multiplying by c, a, and b respectively and adding to get equation 5. Adding equation 4 to 5 times equation 5 eliminates a and reveals that b = 2c. Substituting b = 2c into equation 4 gives a = 3c. We then substitute a = 3c and b = 2c into b²-ca = 6 to find c, and recover a, b, x, y, and z completely. Every step is explained clearly from start to finish. The strategic multiplication-and-addition moves are the entire heart of this solution — by choosing the right multipliers for each equation before adding, we create a system that yields the ratios a:b:c directly, after which everything else follows in one substitution. What you will learn: How x=a², y=b², z=c² eliminates all radicals from the system How multiplying by b, c, a respectively and adding gives equation 4 How multiplying by c, a, b respectively and adding gives equation 5 How adding equation 4 to 5 times equation 5 eliminates a and gives b=2c How substituting b=2c into equation 4 gives a=3c How to find c from b²-ca=6 and recover x, y, and z This type of perfect square substitution combined with strategic equation multiplication appears in the most challenging math olympiad competitions, international mathematics contests, IB Mathematics Higher Level, A-Level Further Mathematics, and university entrance examinations. The ability to choose multipliers that create useful cancellations when equations are added is one of the most sophisticated and elegant skills in competitive mathematics. If this gave you that deeply satisfying feeling where a complex three-variable system suddenly becomes completely transparent, give it a thumbs up, share it with someone who loves elegant algebra, and subscribe for weekly videos on algebra, number theory, calculus, and olympiad problem solving. Hit the notification bell. The next problem might surprise you even more. Don’t forget to like 👍, subscribe @nonsomaths, and hit the notification bell for more math tips and tricks! #maths #algebra #exam