Ketaksamaan Hasil Kali

Diketahui xi > 0 untuk i = 1, 2, … , n, dan x1×x2× ··· ×xn = 1. Buktikan bahwa

Petunjuk. Gunakan ketaksamaan RA-RG.

*

Bandung, 06-10-2017

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3 comments

  1. Karena x_1, x_2, x_3,…,x_2 >0, maka berdasarkan ketaksamaan RA-RG,
    (1+x_1) > = 2.akar(x_1)
    (1+x_2) > = 2.akar(x_2)
    (1+x_3) > = 2.akar(x_3)
    .
    .
    .
    (1+x_n) > = 2.akar(x_n)
    Jadi kita punya
    (1+x_1)(1+x_2)(1+x_3)…(1+x_n) > = 2^n.akar(x_1x_2x_3…x_n)
    karena x_1.x_2.x_3…x_n = 1, maka
    (1+x_1)(1+x_2)(1+x_3)…(1+x_n) > = 2^n

    Like

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