@@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.
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
@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
move x^1/2 to the right side at first, and then square both sides.
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Thanks
Welcome
Как всегда, длинно, путанно, нерационально, с ошибками, но ответ получен правильный
@@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.
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
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Using the look and see method, it's obvious x = 16
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.
@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