A great math question that looks complicated

What do you think about this question? If you're reading this ❤️. Have a great day!

Hello My Friend ! Welcome to my channel. I really appreciate it!
@higher_mathematics

#maths #math

[detroitpolak]

I understood everything up until he started.

[Alekosssvr]

Better - and MUCH easier (no quadratics) to write out x=a+bi and y=c+di and work out values of a, b, c, d.
Realize immediately
1. b+d=0
2. ad+bc=0
3. ac-bd=36
4. a+c=6
1 and 2 give
b=-d
a=c
Then 4 gives
a = c = 3
Substituting into the 3 we get b=-d=sqrt27
No quadratics. CLEAN solution.

[michaelccopelandsr]

This just makes me sad. I used to speak and write math. Now, I can barely follow along and just get the jist of it.

[RayArias]

The solution is a pair of complex conjugates, 3 ± 3i✓(3), so it doesn't matter which variable has which exact complex number as long as the other variable holds its conjugate.

[bellyillish]

So "backwards c" times "regular c" plus y equals 6. Ok I'm with you so far...

[higher_mathematics]

Thank You for watching! Have a great day! Much love and respect❤❤❤ What do you think about this solution?

[jackmoon]

I like maths, but hate those kind of results

[carlosclaptrix]

No solution in non-i domain.
The biggest product of xy would be if both would be equal, so both would be 3. Ergo: 9 is the greatest possible product xy.

[Alekosssvr]

Also an example of how working with complex numbers can sometimes be EASIER than working with real numbers

[theoneaboveall]

Ppl don’t realize he used simple numbers to teach the basics. Of course you can solve this much easier but that was t the point . The point was to teach the basic that you could use for any numbers. 🙄🤦‍♂️

[etisopporm]

Did you know, 4xy= (x+y)² - (x-y)²
Now, if xy = 36, x+y = 6....(i)
then, (x-y)² = -108
or, x-y = (ii)

add (i) and (ii)
x = 3 +3i√3
y = 3 -3i√3

[slshusker]

This video reinforces the reason why I tested out of Algebra in college.

[rainerzufall]

Next video, where you didn't use symmetry! x and y are interchangable! When you know the solutions for x, those for y are the same, just not in the same cases! When x_1 = s1, then y_1 = s2. When x_2 = s2, then y_2 = s1. Or { x, y } = { s1, s2 }.
Maybe more intuitively:
x = 3 +/- 3 sqrt(3) i
y = 3 -/+ 3 sqrt(3) i

[fernandagoncalvesoliveirab]

I understood everything until he started making up stuff.

[David-Suquamish]

If the answer is limited to Real numbers; there is no solution. Once seeing sqrt of a negative, we can just stop and say there is no solution.

[HisHigherness]

🤕 Numbers salad
Glad I'm a Physicist

[okaro]

When a=1 and b is even one can use the pq-formula x = -(p/2) +- sqrtr(p/2)² - q). One gets directly: x = 3² +- sqrt(3²-36).

[GillesF]

Yes, one step to get x and y values, consecutively ...

| x + y = 6 <--- called S (as Sum)
|
| xy = 36 <--- called P (as Product)

/// recall:

• k² - Sk + P = 0 (roots are x and y)

• => k² - 6k + 36 = 0

/// one step (quadratic equation resolution):

k₁ = x = [-(-6) + √((-6)² - 4·1·36)]/2·1 = (6 + 6i√3)/2 = 3 + 3i√3

k₂ = y = [-(-6) - √((-6)² - 4·1·36)]/2·1 = (6 - 6i√3)/2 = 3 - 3i√3

/// final results:

x = 3 + 3i√3

y = 3 - 3i√3



🙂

[stevenfagaly]

When I was 18, this would have been easy. Now, I was fast forwarding to the end.

[Guidussify]

I've watched several of your videos and got this one right on my own! I'm leaning from you. Thanks.