Cara Menyederhanakan Akar pada Matematika
Sederhanakanlah Persamaan Akar Berikut !
$$ 1.\quad \frac{4(2 + \sqrt{3})(2 - \sqrt{3})}{3 + \sqrt{5}} $$
Jawab :
$$ \frac{4(2 + \sqrt{3})(2 - \sqrt{3})}{3 + \sqrt{5}} \times \frac{(3 - \sqrt{5})}{(3 - \sqrt{5})} \\ $$
$$ \frac{4(a-3)(3 - \sqrt{5})}{(9-5)} \\ &= (3-\sqrt{5}) \ $$
(UN 2010 Paket A)
$$ 2. \frac{6(3 + \sqrt{5})(3 - \sqrt{5})}{2 + \sqrt{6}}$$
Jawab :
$$ \frac{6(3 + \sqrt{5})(3 - \sqrt{5})}{2 + \sqrt{6}} \times \frac{(2 - \sqrt{6})}{(2 - \sqrt{6})} $$ $$ \frac{6(9-5)(2 - \sqrt{6})}{(4-6)} \\ &= (-24 + 12\sqrt{6}) \ $$
(UN 2010 Paket B)
Jawab :
$$ \frac{4(2 + \sqrt{3})(2 - \sqrt{3})}{3 + \sqrt{5}} \times \frac{(3 - \sqrt{5})}{(3 - \sqrt{5})} \\ $$
$$ \frac{4(a-3)(3 - \sqrt{5})}{(9-5)} \\ &= (3-\sqrt{5}) \ $$
(UN 2010 Paket A)
$$ 2. \frac{6(3 + \sqrt{5})(3 - \sqrt{5})}{2 + \sqrt{6}}$$
Jawab :
$$ \frac{6(3 + \sqrt{5})(3 - \sqrt{5})}{2 + \sqrt{6}} \times \frac{(2 - \sqrt{6})}{(2 - \sqrt{6})} $$ $$ \frac{6(9-5)(2 - \sqrt{6})}{(4-6)} \\ &= (-24 + 12\sqrt{6}) \ $$
(UN 2010 Paket B)
Komentar
Posting Komentar