# Solving equations using square roots

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In algebra, one of the most important concepts is Solving equations using square roots. Clem's law There are two preconditions for solving the equations with Clem's law, one is that the number of equations should be equal to the number of unknowns, and the other is that the determinant of the coefficient matrix should not be equal to zero. Solving equations with cram's rule is actually equivalent to solving linear equations with the inverse matrix method, which establishes the relationship between the solution of linear equations and its coefficients and constants. However, since n + 1 n-order determinants need to be calculated when solving, the workload is often very large, so cram's rule is often used in theoretical proof and rarely used for specific solutions. For the 3D problem, its essence is to solve the elastic mechanics problem with 6 independent stress components (shear stress is equal to each other), 6 independent strain components and 3 displacement components. This problem can be solved by simultaneous equilibrium equations (3), geometric equations (6) and physical equations (generalized Hooke's law, 6).

The application questions take the polyhedral teaching aids design as the context, guide the examinees to think and operate with their brains, solve practical problems with their mathematical knowledge, and feel the sense of achievement and achievement of serving others and society. Mathematics learning is not only the accumulation of knowledge, but also the formation of rational thinking. The test paper has made progress in stability. On the premise of overall stability, a certain number of innovative questions have been set. These questions test the ability of examinees to analyze and solve problems by creating new problem situations.

We then maximize the determinant of the matrix to make the elements in it different. Here, the determinant of a matrix does not consider the relationship between certain two column vectors alone, but deals with the whole world. There are many ways to solve equations. I found that one of the more common and similar to determinant transformation is to expand or contract one equation several times and add it to other equations.

In the algebra stage, I think the most important thing is to develop your mathematical modeling ability. Solving algebraic equations is just a step-by-step and practice makes perfect operation. However, how to transform practical problems into algebraic solvable abstract problems is a more challenging and practical task. Mathematical modeling is not necessarily very important to the exam (because most of the math exam focuses on solving), but in real life, especially in scientific research of science and engineering, mathematical modeling ability is a hard core ability. If a simpler and more accurate mathematical model can be established, it will almost be the final victory, and the rest of the solution will be left to the computer.

The most important property of the relationship between the three sides of a triangle is that the sum of the two sides is greater than the third side, and the difference between the two sides is less than the third side. This is an important judgment on whether the three sides of a triangle can form a triangle. In the actual application process, instead of directly determining whether a triangle can be formed, we seek the range of the third side, the relationship between the longest side, the shortest side and the perimeter, and so on. These are the actual inspection methods and corresponding questions for this test point..

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