Question

How do you use the guess and check method?

Answer 1

Hint: Here in this question, we have to explain how to use the guess and check method. "Guess and Check" is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem. It needs more tips and tricks for learning it will discuss in the below section.

Complete step by step solution:
All research mathematicians use guess and check, and it is one of the most powerful methods of solving differential equations, which are equations involving an unknown function and its derivatives. A mathematician's guess is called a "conjecture" and looking back to check the answer and prove that it is valid, is called a "proof." The main difference between problem solving in the classroom and mathematical research is that in school, there is usually a known solution to the problem. In research the solution is often unknown, so checking solutions is a critical part of the process.
"Guess and Check" is a problem-solving strategy that students can use to solve mathematical problems by guessing the answer and then checking that the guess fits the conditions of the problem. For example,
Which of the following is a possible solution for the equation \[{x^2} - 28 = - 3x\]?
The answer choices are 7, 4, 2, 0 and -1.
The answer choices are just numbers. If the problem had variables or other more complex answer choices, this method wouldn't help. To solve this without guess and check, you'd need to set the equation equal to zero, then factor, then solve.
Let's just try plugging in numbers. Let's start with the middle number, 2:
\[ \Rightarrow \,\,{2^2} - 28 = - 3\left( 2 \right)\]
\[ \Rightarrow \,\,4 - 28 = - 6\]
\[ \Rightarrow \,\, - 24 = - 6\]
It looks like 2 is too small, so let's try going larger and use 4:
 \[ \Rightarrow \,\,{4^2} - 28 = - 3\left( 4 \right)\]
\[ \Rightarrow \,\,16 - 28 = - 12\]
\[ \Rightarrow \,\, - 12 = - 12\]
Hence, 4 is the correct answer.

Note: Use the "Guess and Check" strategy. Guess and check is often one of the first strategies that students learn when solving problems. This is a flexible strategy that is often used as a starting point when solving a problem, and can be used as a safety net, when no other strategy is immediately obvious.