Anything is possible, unless it's not

Saturday, November 13, 2010

Can you solve these problems?

(Problem 1.) Given real constants a, b, c, ... , z
that satisfies a5 = b; b5 = c; c5 = d; ... ; y5 = z
If a = 2010, find the value of (x-a)(x-b)(x-c)...(x-z).

(Problem 2.) Find the value of cos(1) cos(2) cos(3) ... cos(2010).
Note: cosines are expressed in degrees, not radians.

(Problem 3.) x2 + x + 1 = 0 have two complex solutions, a and b.
Find the value of a(28081996+17081945) + b(24031995+1113636363636)

(Problem 4.) If x is a positive real number,
what is the minimum value of xx ?
Express the answer in terms of e (Euler's constant).

2 comments:

  1. Problem 1. perhatikan ada faktor ( x - x) = 0. maka jawabannya 0

    Problem 2. Perhatikan bahwa cos 90 = 0. maka jawabannya 0

    Problem 3. jawabannya 1 + 1 = 2

    Problem 4 : misalkan y = X^x. maka ln y = x ln x. i/y dy = (1 + ln x) dx. maka dy/dx = y( 1 + ln x ). nilai minimum saat dy/dx = 0. maka karena y tidak sama dengan 0, maka 1 + ln x = 0. ln x = -1. x = 1/e. maka nilai minimum dari X^x = (1/e)^ ( 1 /e)

    haha
    -johan chrisnata-

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  2. Dewanya dewa jawab... jelas pasti benar semua

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