Cambridge Test | Can You Solve?

Hello. In this video, i am going to show you a great Algebra question that you can use to practice your math skills. This question is sure to challenge your algebra knowledge, so make sure you practice this trick today! With practice, you'll be able to tackle any algebra problem with ease!

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[mr.d]

I haven't watched it yet, but here is my solution:
Assume we can write √(3-2√2) in the form √a-√b, where a is greater than b. (Since the value is positive.) So we have:
√(3-2√2) = √a-√b, square both sides,
3-2√2 = a-2√(ab)+b, rearranging the terms, we get
3 - 2√2 = a+b - 2√(ab). We can see that the two sides are in the same form, so we have a system of equations:
a+b=3 and a*b=2. You can probably guess the answer, but let's just substitute b=3-a into the second equation. So we get:
a*(3-a)=2
3a-a²=2
-a²+3a-2=0. At this point, we could use the quadratic formula, but it's unnecessary because the expression can be factored easily:
-a²+3a-2=0
-a²+a+2a-2=0
-a*(a-1)+2*(a-1)=0
(a-1)*(2-a)=0. So if a-1 = 0, then a=1 and if 2-a = 0, then a=2. Now this whole procedure can be done for b and we want a to be the bigger number, so we have a=2 and b=1.
So our solution is:
√(3-2√2) = √2-√1 = √2-1. We can easily check if the two are the same by squareing both sides, and we get:
3 - 2√2 = 2 - 2√2 +1 which is true, so we have our solution.*

[AyushJaz]

man i solved it in my mind in 3 seconds. 💀💀 cambridge is too easy ig

[drziggyabdelmalak]

I always thought terms and so on had to keep balanced, and what you do to one thing or side you have to do to the other side? How can you just call 2 (the square root of two) squared, and 1 (1 squared) but leave 'two root two' as it is?

[Swaroop]

This was a nice question, I also solved it, I have a book which has so many types of question and it is one of them

[supratiksahoo]

Uhm is this a question meant for grade 6 students?