Germany | Can you solve this? | Math Olympiad

[@joserivas5059]

Thanks

[@MasterTMathsClass]

Welcome

[@СергейИванчиков-р8д]

Как всегда, длинно, путанно, нерационально, с ошибками, но ответ получен правильный

[@1234larry1]

@@СергейИванчиков-р8д I only saw one error that he made and he corrected it. It was interspersed with many fundamentals, but that is OK because it is a teaching video.

[@jeffzheng1913]

move x^1/2 to the right side at first, and then square both sides.

[@MasterTMathsClass]

✌️

[@insteresting]

Solve the equation
√x + √(x - 12) = 6 (i)
Let u = √x and v = √(x - 12):
u² = x
v² = x - 12
v² = u² - 12
u² - v² = 12 (ii)
So (i) becomes
u + v = 6 (iii)
Factor the difference of squares in (ii):
(u - v)(u + v) = 12
(u - v) * 6 = 12
u - v = 12/6
u - v = 2 (iv)
With (iii) and (iv), you get the following system:
u + v = 6
u - v = 2
which gives you
(u + v) + (u - v) = 6 + 2
2u = 8
u = 8/2
u = 4
Square both sides:
u² = 4²
u² = 16
Substitute back u² = x so you get the solution:
x = 16

[@MasterTMathsClass]

✌️

[@NoTimeForCheats-pg2lu]

Using the look and see method, it's obvious x = 16

[@1234larry1]

Guessing is fine for fairly simple problems like this, but the idea is to learn the fundamentals of algebra, because sometimes guessing won’t work.

[@NoTimeForCheats-pg2lu]

@1234larry1 it wasn't a guess, careful analysis of the problem using the look and see method yielded the correct answer, learning processes isn't enough to solve maths problems, one needs intuition and critical thinking skills