When do we have sqrt(a+b)=sqrt(a)+sqrt(b) скачать в хорошем качестве

When do we have sqrt(a+b)=sqrt(a)+sqrt(b)

Today, we're gonna prove one of the most beautiful inequalities In mathematics. It's the Triangular inequality. So, basically, what we need to prove is to show that the absolute value of x plus y, is less than or equal to the absolute value of x. Plus the absolute value of y. This is a very fundamental result in linear algae, in the linear analysis, in studying calculus and improving theorems. So this is very useful. When we are trying to prove some theoretical examples, We will see that we can use this result to prove many of the ideas that we will see. So one of the keys here is that we can use the fact that the absolute value of x is always positive. If x is positive, it's positive. If x is negative, we make it positive by inserting a minus here to make it positive. This problem can be beneficial to student doing calculus to student doing, AP calculus, and to student trying to get to the Olympia or to teachers trying to get their licensure in mathematics for high school teachers. Also, it's great for students who are willing to work or struggling with mathematics or trying to find the tricks. And learning ideas. How to prove this is basically a basic introduction to proves. We will see how to do this and how to make profit of this triangular inequality. We will use it later to prove. Many of the ideas concerning limits, derivatives and integrals. Also, solving logarithmic equations is very important. We need to make sure that the domain of logarithmic functions is, well, defined. So we know that the natural logarithm is defined when X is positive. So we have the plural parties of the log, like, the log of the product, is the sum of the, the logs. Also, the log of the ratio is just the log of a minus, the log of B. This is very important in solving problems, So will you? That's what we're gonna see today. We can use all the result that we have done so far to prove the norms To prove the triangular inequality for some Norms in this problem. We're going to prove one of the triangular inequalities for one of the norms, We can use the function f of T. It was T over 1 plus C to share this result, but we are not able to do that. We're gonna use some basic properties of the absolute value. To prove this result, this is one of the main result That we need in calculus and dealing with Metric properties of this simple spaces. The aim of this problem is to find the minimum value of a number and its inverse, We can do this problem by doing many properties of algebra 2, but the good thing is that we can use the square root of this value and solve. When can we say that the square root of the sum of two numbers is equal to the sum of the square roots? Assume that the square roots are defined for positive numbers And the sum is defined for positive numbers. In general. We don't have the sum of the square. Root is equal to the sum of the roots, so that's no true in general. Except one of the element is zero. So this proof, we're gonna present a proof of this result concerning the square. Root of the sum of the values And we're gonna show by giving some contra examples. Why? This one is not true in general. #python #olympiad #maths