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Jika 0 < b < a dan a² + b² = 6ab, nilai dari :
frac{a + b}{a - b} =
Silahkan….

Kalau ngga ngerti jangan jawab..!!!
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Jawaban:

(a+b)² = 2ab = 6ab

(a+b)² = 8ab

a+b = √8ab

(a-b)² = a²+b²-2ab

= 6ab-2ab

= 4ab

a-b=√4ab

(a+b)/(a-b) = √8ab/√4ab = √2

begin{array}{rcl}a^2+b^2&=&6ab\~\(a+b)^2-2ab&=&6ab\~\(a+b)^2&=&8ab\~\a+b&=&sqrt{8ab}\~\~\~\a^2+b^2&=&6ab\~\(a-b)^2+2ab&=&6ab\~\(a-b)^2&=&4ab\~\a-b&=&sqrt{4ab}end{array}

Sehingga :

begin{array}{rcl}frac{a+b}{a-b}&=&frac{sqrt{8ab}}{sqrt{4ab}}\~\&=&sqrt{frac{8ab}{4ab}}\~\&=&sqrt{2}end{array}