Solving a radical equation in two ways

This video is about a radical equation. Two methods are shown.
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#ChallengingMathProblems #RadicalEquations #Algebra

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[SyberMath]

Event though this problem can be considered a typical textbook problem, the second solution method is pretty interesting and probably not very well known! Radical equations are simply awesome! I like the second method better. What are your thoughts?

[michaelempeigne]

You made a sign error in one of the solutions after using quadratic formula

[CaradhrasAiguo]

I chose a different substitution to make the arguments to the roots symmetric, i.e. u = x^2 + 6x + 7/2, as that's the mean of 11 and -4; squaring will result in a difference of two squares and the 7/2 canceling outside the radical, leading to 25 - 2u = sqrt(u^2 - (15/2)^2)

The second method at 6:56 is quite neat regardless!

[VSN]

I really like the second method although the sad thing is that it only works if the second degree and first degree terms are exactly the same. Nice video overall

[dzpismu]

I always like to do substitution first. Some time it is really powerful.
Name the first root as a, second root as b
b = 5 - a
a*2 - b*2 = 15
a*2 - 25 + 10a - a*2 = 15
10a = 40
a = 4
x*2 + 6x + 11 = 16
x*2 + 6x - 5 = 0
Then we get the same solutions as you got.
How do you like this simple method?

[sugamsharma]

I will personally prefer second way.

Nice video👌👌

[itzrealzun]

'Everything is awesome' - song from LEGO Movie)

[elmoussadekelaoufir]

I have very admirate the second method il's magical. Good job teacher..

[ularaippanjin]

if both √(X^2+6x+11) and √(x^2+6x-4) are integers, then letting u=x^2+6x-4 ; u=n^2 and u+15=m^2, m+n=5 so u=1, n=1, m=4.
although this is not a precise logic as they might be transformed to a+√b and (5-a)-√ b

[vuyyurisatyasrinivasarao]

Good Second method is very logic....how this idea will come us great Ur sir

[scottleung]

I almost got the right solutions, but somewhere down the road my signs became messed up.

[vcvartak]

second method is good but you can use here because coefficients of x and x(square) are same in both terms. I don't understand why you need to frequently change the colors

[LOL-gnkv]

Great video like always but small mistake at 5:08 i think the first solution is root14- 3