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DIKETAHUI

$sf a +b +c =0$

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DITANYA

$sfdfrac{(a + b)(a + c)(b + c)}{abc} =...?$

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JAWAB

$sf a +b +c =0 implies a +b = -c$

$sf a +b +c =0 implies a +c= -b$

$sf a +b +c =0 implies b+c= -a$

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Sehingga:

$begin{aligned}sfdfrac{(a + b)(a + c)(b + c)}{abc}&=sfdfrac{(-c)(-b)(-a)}{abc} \&=sfdfrac{-abc}{abc}\&=sf-1end{aligned}$

Jawaban:

$frac{(a + b)(a + c)(b + c)}{abc} = frac{ ( - c)( - b)( - a)}{abc} = frac{ - abc}{abc} = - 1$

Penjelasan dengan langkah-langkah:

$a + b + c = 0 \ - a = b + c \ - b = a + c \ - c = a + b$