Jika: - Universityku

$huge frac{1}{a} + frac{1}{b} = frac{3}{7}$
nilai a² + b² = …

Jika:

Jawab:

Penjelasan dengan langkah-langkah:

$displaystyle dfrac{1}{a}+dfrac{1}{b} = dfrac{3}{7}\\ dfrac{a+b}{ab}= dfrac{3}{7}\\7(a+b) = 3ab\49(a^2+b^2+2ab) = 9a^2b^2\ boxed{boxed{a^2+b^2 = dfrac{9}{49}a^2b^2-2ab = dfrac{ab(9ab-98)}{49}}}$

Kalau yang anda tanyakan merupakan sistem diophantine :

$7(a+b) = 3ab to a+b = 3m, ab = 7m\a(7-3b)+7b = 0to a = dfrac{7b}{3b-7}, ab = 7m to a = dfrac{7m}{b}\dfrac{3b^2}{3b-7} = 3m\\b^2- 3mb+7m = 0\\b = dfrac{3mpm sqrt{9m^2-28m}}{2}\\a = dfrac{14m}{3mpmsqrt{9m^2-28m}} = dfrac{3mmp sqrt{9m^2-28m}}{2}\$

$a^2+b^2= dfrac{ab(9ab-98)}{49} = dfrac{28mcdot (9cdot 28m-98)}{196}\\boxed{boxed{a^2+b^2=9cdot 4m - 14 = 36m-14 = 2(18m-7), minmathbb{Z} }}$

Jawab:

Penjelasan dengan langkah-langkah:

1/a + 1/b = 3/7

kaliin kedua ruas dengan 7ab :

7a+7b = 3ab

(7a+7b)^2 = 9(ab)^2

49a^2+49b^2+49ab = 9(ab)^2

49(a^2+b^2) = 9(ab)^2 – 49ab

a^2+b^2 = 9/49 * (ab)^2 – ab