maths question...好少...IDENTITY(5分)

[匿名]

2008-07-17 6:07 pm

Please answer ALL the question:

1)Here is a magician and a teenager conversation:

FIRST CONVERSATION:
Magician:"Subtract 5 from your age.Then multiply the difference by the sum of two times your age and 10.finally subtract the square of your age from the product.Tell me the result and I'll tell your age."

Teenager:"The result is 350."

SECOND CONVERSATION:
Magician:"That mean the square of his age minus 50 is 350..........You are 20 years old."

Teenager:"Wow!You're so amazing!"

QUESTIONS:

A.)Let x be he age of the teenagerand R be the result of the operation.Write down an equation to express the relationship between x and R according to the instructions given by the magician in The first coinversation.

B.)
(i)Suggest an identity that the magician uses to find the age of the teenager.Explain how the magician can obtain the age of the teenager.

(ii)Can the magician use the identity in part(i)to find other people's ages?Explain ypur answer briefly.

回答 (1)

Uncle Michael

2008-07-17 7:02 pm

✔ 最佳答案

A.)
R = (x-5)(2x+10)-x2

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B.)(i)
R = (x-5)(2x+10)-x2

R = (x-5)2(x+5)-x2

R = 2(x2-25)-x2

R = 2x2-50-x2

R = x2-50

x2 = R+50

x = √(R+50)

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B.)(ii)
Yes, the magician can used the identity in part(i) to find other people’s ages.

Identity used to calculate R from x (the age):
R = (x-5)(2x+10)-x2

Identity that the magician uses to calculate the age:
x = √(R+50)

These two identities are identical. The first one is to express R in terms of x, and the second one is to express x in terms of R. Therefore, when R is calculated from x using the first identity, x should be calculated from R using the second identity.
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