Please help solve the following math problem (about golden section). Thank you-- It is known that the length of AB is the following sign 10, and C is divided into two parts: AC = (five times of the following sign 2 - root sign 10) / 2, BC = (three times of the root sign 10 - five times of the root sign 2) / 2 Verification: C is the golden section of line AB (write the specific process)

Please help solve the following math problem (about golden section). Thank you-- It is known that the length of AB is the following sign 10, and C is divided into two parts: AC = (five times of the following sign 2 - root sign 10) / 2, BC = (three times of the root sign 10 - five times of the root sign 2) / 2 Verification: C is the golden section of line AB (write the specific process)

AC/BC=[(5√2-√10)/2] /√10 = (√5-1)/2
That is the golden section ratio, which makes AC ^ 2 = BC * ab

What is the golden section

The golden section, also known as the golden rule, refers to a certain mathematical proportional relationship between the parts of things, that is, the whole is divided into two parts, the ratio of the larger part to the smaller part is equal to the ratio of the whole to the larger part, and the ratio is 1 ∶ 0.618 or 1.618 ∶ 1, that is, the ratio of 0.618.0.618 of the whole section is considered to be the most aesthetically significant, So it is called golden section

If point C makes line AB golden section, and AC > BC, AC = 2cm, then BC=______ ．

∵ point C is the golden section point (AC ＞ BC) of line AB, ∵ AC = 5 − 12ab, AC = 2cm, ∵ AB = (5 + 1) cm, ∵ BC = AB-AC = 5 + 1-2 = (5-1) cm