Can you solve this Golden Math Problem ? скачать в хорошем качестве

Can you solve this Golden Math Problem ?

This problem is great since it not only uses useful areas of mathematics is also a good example of problem decomposition that is breaking a problem into simpler parts. Reference:    • A Golden Answer   https://www.mathsisfun.com/algebra/qu... Script: Hello Everyone and welcome to another interesting Math problem. This problem is great since it not only uses useful areas of mathematics is also a good example of problem decomposition that is breaking a problem into simpler parts. Lets begin - Here is the problem. 4 to the power x + 6 to the power x is equal to 9 to the power x Solve for x. Please pause the video and solve. If you do not wish to solve the problem, just write down your approach or what thoughts are running through your mind. I encourage you to do so. Ok, now here is one solution Let us try to simplify things. Rather than x in 3 places, let’s try to have x in 2 places. And one of way of doing so is dividing both sides by 4 to the power x. This is what we get . Now this first term gives us 1 The second term can be written as 3 by 2 to the power x. And this third term can be written as 3 by 2 to the power 2 x. Please make sure that this is clear - how we got 2x. Ok, now lets focus on this term here - 3 by 2 to the power x. Let us make it disappear for the moment. And we do so by introducing a new variable - y And let y = 3 by 2 to the power x. Using ‘y’ in the above equation. This is what we get. Now suddenly our problem looks much simpler. And we also have a quadratic equation. Let us move all these elements to one side. We get Y square minus y - 1 is equal to 0. Now let us solve for y using the quadratic equation formula Now we have 2 values: One value is greater than zero, and one is less than 0. Now only one value will work in our solution. Can you guess which one and why? The answer is this one - which is greater than zero. But wait , we are not done as yet. We have to calculate x and not y, remember. So we have: 3/2 to the power x = 1 + sqrt(5) / 2 Now this can be solved using logarithms. So using logarithms to solve for x we get X = log ( 1 +sqrt(5) / 2) to the base 1.5. Using natural logs, this can be written like so X = ln ( 1 + sqrt(5) / 2) / ln (1.5) And using a calculator to solve the approximate answer is 1.19! Is this what you got? If not write down your answer in the comment section. Guys, this problem appeared in a famous competitive exam. I liked this problem since it involves quadratic equations, logarithms and was very satisfying to solve. I hope you enjoyed it too.