Do you know the beauty of the combination of numbers and shapes? Maybe you used the idea of algebra when you did the geometry problem, but did you use the idea of geometry when you did the algebra problem?

What is the minimum direct sum of (1) radical sign (x+4) and radical sign (x-24x+ 153)?

(2) If a, b and c are nonnegative real numbers, it is proved that the sum of the radical number (A+B) and the radical number (B+C) and the radical number (C+A) is greater than or equal to twice the radical number (a+b+c).

(3) Through the above inquiry, can you sum up when to use the auxiliary number?

(4) The following question is not simple. The idea of combining numbers and shapes reflects a very in-depth problem. Give it a try!

Let x, y and z be positive numbers, and prove: root number (x+y)+ root number (x+z-xz).

Greater than or equal to the root sign (y+z+yz is three times the root sign)

(5) You are really good, but many times the shape of the auxiliary number can't be solved by several straight lines. The following question is much more difficult than the last one!

If a, b, x and y are all real numbers, and A2+B2 = 1, X2+Y2 = 1. Proof: AX+BY ≤ 1.

If you want to see the answer, click Resources.