Triangle Inequality: (Bangladesh Online Math Camp)
Re: Triangle Inequality: (Bangladesh Online Math Camp)
Anybody solved the exercise 1.10?
Re: Triangle Inequality: (Bangladesh Online Math Camp)
I was explaining your third case. So $y \geq 0$
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Re: Triangle Inequality: (Bangladesh Online Math Camp)
আমি মোবাইল থেকে ব্যাবহার করি তাই latex ব্যাবহার করতে পারিনা।
(উল্লেখ্য আপনার latex ব্যাবহার করে যে ইকুয়েশন গুলো লেখেন সেগুলো আমার মোবাইলে বিদঘুটে কিছু চিহ্ন আকারে দেখা যায়।এর কোন প্রতিকার আছে?)
(উল্লেখ্য আপনার latex ব্যাবহার করে যে ইকুয়েশন গুলো লেখেন সেগুলো আমার মোবাইলে বিদঘুটে কিছু চিহ্ন আকারে দেখা যায়।এর কোন প্রতিকার আছে?)
Re: Triangle Inequality: (Bangladesh Online Math Camp)
@toweikul
assume without loss of genarility,x greater than or equal y then (x)^1/2 is greater than or equal (y)^1/2
now consider two set,A={x,y} and B={(x)^1/2,(y)^1/2}
using rearrangement inequality,x(x)^1/2+y(y)^1/2 is greater than or equal x(y)^1/2+y(x)^1/2=(x)^1/2*(y)^1/2((x)^1/2+(y)^1/2)
assume without loss of genarility,x greater than or equal y then (x)^1/2 is greater than or equal (y)^1/2
now consider two set,A={x,y} and B={(x)^1/2,(y)^1/2}
using rearrangement inequality,x(x)^1/2+y(y)^1/2 is greater than or equal x(y)^1/2+y(x)^1/2=(x)^1/2*(y)^1/2((x)^1/2+(y)^1/2)
Re: Triangle Inequality: (Bangladesh Online Math Camp)
This inequality is taught in class eleven in real numbers. But no teacher ever told us that it is called The Triangle inequality!
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Re: Triangle Inequality: (Bangladesh Online Math Camp)
It is called the triangle inequality because it can also be represented as the form of the classic geometric inequality ,
for $\triangle ABC$, sum of any two sides is greater than the third.
for $\triangle ABC$, sum of any two sides is greater than the third.
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Re: Triangle Inequality: (Bangladesh Online Math Camp)
Could u plz state the problem 1.10 (i'm in the class & apart from the book right now ) ?
 nafistiham
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Re: Triangle Inequality: (Bangladesh Online Math Camp)
unfortunately, i couldn't solve this problem $1.10$ .again stating the problem for mugdho.snigdho and myself.hoping to get some hint
if $x,y> 0$, then prove that $\sqrt{\frac{x^{2}}{y}} + \sqrt{\frac{y^{2}}{x}}\geqslant \sqrt{x}+\sqrt{y}$
if $x,y> 0$, then prove that $\sqrt{\frac{x^{2}}{y}} + \sqrt{\frac{y^{2}}{x}}\geqslant \sqrt{x}+\sqrt{y}$
\[\sum_{k=0}^{n1}e^{\frac{2 \pi i k}{n}}=0\]
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Re: Triangle Inequality: (Bangladesh Online Math Camp)
Tiham,
Would you like some hints?
Here are some if you want...
Would you like some hints?
Here are some if you want...
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."  Sherlock Holmes
Learn how to write equations, and don't forget to read Forum Guide and Rules.
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth."  Sherlock Holmes
Re: Triangle Inequality: (Bangladesh Online Math Camp)
To solve the proble 1.10, you have to define two case while $x \geq y$ and $x<y$ and u can try by squaring two side.
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