Math Olympiad | Can you solve given System of Equations ? | 95% Failed to Solve!

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#matholympiad #maths #systemofequations #algebra

[JPTaquari]

Visually, in less than a minute, we see that the possibility set is 4, 1, 1
X can be 4; Y = 1 ; Z = 1;
Y can be 4; X = 1 ; Z = 1;
Z can be 4; X = 1 ; Y = 1;

I tried to find the values ​​by developing the equations, but I didn't find a successor. Now I'm going to see your magic!!!!

[uekxmpg]

Consider
a=x½, b=y½, c=z½ and eq
a+b+c=4,
a²+b²+c²=6,
a⁴+b⁴+c⁴=18
a, b, c are nonnegative

By the routine calculations, ab+bc+ca=5, abc=2. So {a, b, c}={1, 1, 2}.
Thus, {x, y, z}={1, 1, 4}.
Note that { } is a set symbol.

[허공]

13:38 it is easy to use SDM instead of long division.

[ranjanghosh]

How do you get the cubic equation of m?

[sumit-mnys]

Great effort for solving the solution Thanks 👍