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。