The mathematician Girolamo Cardano is credited with the first use (in 1545) of negative square roots in
Question:
The mathematician Girolamo Cardano is credited with the first use (in 1545) of negative square roots in solving the now-famous problem, “Find two numbers whose sum is 10 and whose product is 40.” Show that the complex numbers
satisfy the conditions of the problem. (Cardano did not use the symbolism i√15 or even √ - 15. He wrote R.m 15 for √ - 15 meaning “radix minus 15.” He regarded the numbers 5 + R.m 15 and 5 - R.m 15 as “fictitious” or “ghost numbers,” and considered the problem “manifestly impossible.” But in a mathematically adventurous spirit, he exclaimed, “Nevertheless, we will operate.”)
5 + i√15 and 5 - iV15
Step by Step Answer:
Sum 5i15 5i15 5...View the full answer
Related Video
The square of a number is the result of multiplying that number by itself. This is also known as \"raising a number to the power of 2\" or \"squaring a number\". The concept of squaring a number is important in many areas of mathematics and science, including geometry, trigonometry, and physics. It is also used in computer programming and data analysis. The square of a number is always positive, except for the square of 0, which is 0. When a negative number is squared, the result is positive. For example, the square of -3 is 9, since (-3) x (-3) = 9. To square a two-digit number, you can use the following formula: (A x 10 + B)^2 = A^2 x 100 + 2AB x 10 + B^2 Where A represents the tens digit and B represents the ones digit of the two-digit number. In this video, you can learn a fascinating math technique to quickly compute the square of any two-digit number. This trick involves three simple steps that enable you to arrive at the answer in a matter of seconds. The video demonstrates this method using three different examples, and you can try it out yourself and share your score in the comments section. You can also see how other students are performing using this technique.
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