You could also multiply both by x and have: x^2 + y^2 >= 2xy Subtracting both sides by 2xy you get: x^2 - 2xy + y^2 >= 0 And finally this equals to (x-y)^2 >= 0 The left term is a square which is always not negative, so the equation is true.
Isn't multiplying by x adding a solution you should also mention that x is different from 0 to make this an equivalence if not it will just be an implication and to solve completely you should do the other way around so that S is included in the solutions and the solutions are included in S.
Again thank you soo much for this video , at the same time i follow some books dedicated to olympiad inequalities, Today i want to share this inequalitie with the beautiful community,if:a,b,c are positif numbers and: a+b+c=1 proof that : 1/(b+c) +1/(a+c) +1/(a+b)>=9/2
Keep on releasing these kinds of stuff that uses AI voices of popular people ✨... As a math enthusiast and a supporter of masculinity, this is 'perfect' content 💯...
Do a matrix problem. Heard he has a lot to say about those
You could also multiply both by x and have:
x^2 + y^2 >= 2xy
Subtracting both sides by 2xy you get:
x^2 - 2xy + y^2 >= 0
And finally this equals to
(x-y)^2 >= 0
The left term is a square which is always not negative, so the equation is true.
was my idea as well. i dont understand why they needed that arithmetic-geometric-formula this is sooooo much easier xd
Isn't multiplying by x adding a solution you should also mention that x is different from 0 to make this an equivalence if not it will just be an implication and to solve completely you should do the other way around so that S is included in the solutions and the solutions are included in S.
Thank you, this very helpful 👏🏻👏🏻
Last inequality is just a+b≥2sqrt ab, cyclic product gives (a+b)(a+c)(b+c)≥8sqrt(a^2b^2c^2)=8abc, equality only holds when a=b, a=c, b=c or just a=b=c
Again thank you soo much for this video , at the same time i follow some books dedicated to olympiad inequalities,
Today i want to share this inequalitie with the beautiful community,if:a,b,c are positif numbers and:
a+b+c=1 proof that :
1/(b+c) +1/(a+c) +1/(a+b)>=9/2
Nice one, thank you. Spoiler alert , a hint down below:
.
.
.
.
.
.
.
.
.
.
Think of Cauchy-Schwarz inequality
@@MathWisdom42 i prof it using Nesbitt inequality , i'l try to do it by Cauchy Schwartz, again thank you soo much ,😊😊🌹
Andrew tate, which books do you recommend for maths Olympiad
Keep on releasing these kinds of stuff that uses AI voices of popular people ✨... As a math enthusiast and a supporter of masculinity, this is 'perfect' content 💯...