Bad math, good answer!

Interesting bad question, equation with two square roots, for intermediate algebra students, algebra 2 students, and people who like math!,

good to know for teaching algebra,
blackpenredpen,
math for fun,

[douglasmagowan]

Freshman's dream: (a+b)^2 = a^2 + b^2

[xamzx]

it is just a funny case, for example you have 16/64, you remove 6s in the nominator and the denominator and you get 1/4 which is right

[holymanlogin]

You could notice factorization (6x-9) = 3(2x-3), witch makes correct solving easier.
3(2x-3) = -10sqrt(2x-3); x1=3/2;
3sqrt(2x-3) = -10; 9(2x-3)=100;
18x-27=100; x2=127/18.

[MagnusSkiptonLLC]

If I were really evil (and taught algebra), I would find a whole bunch of examples where √A + √B = √(A + B) and assign them to my class. Then give zeros to people who did it the wrong way.

[_DD_]

what to say:) the procedure is more important than the result.

[NetAndyCz]

I think you could at the end point out that 2x-3=0 so even if you ignored that term completely 8x+13=25 would still give you 8x=12; x=3/2

PS: I really like the way you can work with two pens swwitching colors you use on the fly

[jessehammer]

3:11 My blood pressure rose measurably.

[sbdama]

The Thumbnail has the equation wrong... sqrt(8x-13) should be sqrt(8x+13).

Keep up the great work! I am loving the awesome insight you have! I am sharing a few ideas with my students too!

Great stuff!

[APuZvfvag]

I bought this equation on Aliexpress and forgot to check the reviews, so I got x=127/18. Free shipping, though.

[shivshankaryadav]

You're the best, really like your vids and love your accent
And being a teacher at such a young age is awesome

[OonHan]

when this comes up as the only question in a 100 mark exam paper and you lose 99 marks for method

[jeffreycanfield]

Mistake 1: Me
Mistake 2: My math skills and inability to find the mistakes

[blackloop]

2:09
you so good i wish my math teacher be like you

[Sam_on_YouTube]

You can square both sides, you just have to do it correctly and it doesn't necessarily get you out of squaring it again:
sqrt(8x+13)+sqrt(2x-3)=5
[sqrt(8x+13)+sqrt(2x-3)]^2=25
8x+13 + sqrt(8x+13)sqrt(2x-3) + 2x-3=25
10x + 10 + sqrt(8x+13)sqrt(2x-3)=25
sqrt[(8x+13)(2x-3)]=15 - 10x
sqrt[16x^2-24x+26x-39]=15 - 10x
sqrt(16x^2+2x-39)=15 - 10x
sqrt(16x^2+2x-39)^2=(15 - 10x)^2
16x^2+2x-39 = 225-300x+100x^2
84x^2-302x+264=0

3/2 also solves this quadratic equation.

189-453+264=0

[stumbling]

Secret method for finding square roots: Add up the digits and subtract 3. e.g. sqrt(16) = 1+6-3 = 4, and sqrt(36) = 3+6-3 = 6.

[MisterUnlikely]

You know, the math gets a lot easier when you let U=2x-3. Then 4U+25= 8x+13. Then you can solve sqrt(4U+25)+sqrt(U)=5. You get some really nice cancellation.

[JanStout]

Alternatively, 1st massage sqrt(a) + sqrt(b) = sqrt(c) to get 0 = c^2 - 2(a+b)c + (a-b)^2, then solve with a = 8x-13, b = 2x-3, c = 25.

[davidwright]

Depending on blind chance to get the 'right' answer is always a BAD idea! NO credit -because credit is mostly for showing you know what you're doing - even if you make a sign error or mis-copy a number or something! That's worth quite a bit of credit. The 'right' answer for the 'wrong reason' - won't do. Would you fly on an airplane 'designed 'by chance?? On two or more???

[jacksainthill]

My guess is that there are zero mistakes in the thumbnail because it is exactly as you intended.

[chovie]

lol that quick cut to WolframAlpha factoring page. I felt like someone was calling me out