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The analysis process of several math error-prone problems,
1, let a and b be the equation x-? 12x? +? 9? =? 0, then the value of a+ B under the root sign is _ _

Relationships rooted in coefficients (Vieta theorem);

Answer? +? b? =? 12

Answer? *? b? =? nine

(√a? +? √b)? =? Answer? +? b? +? 2√(ab)? =? 12? +? 2*3? =? 18

√a? +? √b? =? √ 18=? 3√2? -Error-prone places √ 18

2. In Rt△ABC, ∠ c = 90,? AC=4,? BC=3, Rt△ABC is inscribed with a square, and the side length of the square is found.

There are two kinds of discussions,

⑴? C is a point of a square, and the figure can be drawn. Using the ratio, the side length can be found to be 12/7.

Short process

⑵? C is a point that is not a square, so one side of the square is on AB. Draw a picture. Using the ratio, we can find that the side length is 60/37?

Details are as follows:

As shown in the figure, let the side length of the inscribed square be? x? ,

Because AC=4 and BC=3, the hypotenuse AB=5.

It's because of ⊿CDG∽⊿CAB again.

So DC=4x? /? five

Author: ABC Ed

DE/BC=AD/AB

X/3? =? (4? -? 4x/5)? /? five

Solve? x? =? 60/37

So what is the side length of a square? 60/37。