WŁĄCZANIE CZYNNIKA POD I WYŁĄCZANIE PRZED PIERWIASTEK.Wykonaj mnożenie i doprowadź wyrażenia do najp.... Question from @fannybunny

October 2018 2 29 Report

WŁĄCZANIE CZYNNIKA POD I WYŁĄCZANIE PRZED PIERWIASTEK.

Wykonaj mnożenie i doprowadź wyrażenia do najprostszej postaci:

a) $(2\sqrt{6} - 3\sqrt{2})(\sqrt{6}+2\sqrt{2})$

b) $(3\sqrt{6} + \sqrt{3})(4\sqrt{3} - \sqrt{6})$

c) $(\sqrt{10} - 2\sqrt{5})(3\sqrt{10} - 2\sqrt{5})$

d) $(\sqrt{15} - 2\sqrt{3})(\sqrt{15} + \sqrt{3})$

erre

$(2\sqrt{6} - 3\sqrt{2})(\sqrt{6}+2\sqrt{2})=\\ =12+4\sqrt12-3\sqrt12-12=\\ =\sqrt12=2\sqrt3$

$(3\sqrt{6} + \sqrt{3})(4\sqrt{3} - \sqrt{6})=\\ =12\sqrt18-18+12-\sqrt18=\\ =11\sqrt18-6=\\ =33\sqrt2-6$

$(\sqrt{10} - 2\sqrt{5})(3\sqrt{10} - 2\sqrt{5})=\\ =30-2\sqrt50-6\sqrt50-20=\\ =10-6\sqrt50=\\ =10-30\sqrt2$

$(\sqrt{15} - 2\sqrt{3})(\sqrt{15} + \sqrt{3})=\\ =15+\sqrt45-2\sqrt45-6=\\ =9-\sqrt45=\\ =9-3\sqrt5$

2 votes Thanks 2

mrsmalik7

a) $(2\sqrt{6} - 3\sqrt{2})(\sqrt{6} + 2\sqrt{2}) = 12 + 4\sqrt{12} - 3\sqrt{12} - 12 = \sqrt{12} = 2\sqrt{3}$

b) $(3\sqrt{6} + \sqrt{3})(4\sqrt{3} - \sqrt{6}) = 12\sqrt{18} -18 +12- \sqrt{18}$ $= 11\sqrt{18} -6 = 33\sqrt{2} - 6$

c) $(\sqrt{10} -2\sqrt{5})(3\sqrt{10}-2\sqrt{5}=30-2\sqrt{50}-6\sqrt{50}+20=$ $50 - 8\sqrt{50}=50-40\sqrt{2}$

d) $(\sqrt{15}-2\sqrt{3})(\sqrt{15}+\sqrt{3})=15+\sqrt{45}-2\sqrt{45}-6=9-\sqrt{45}$ $=9-3\sqrt{5}$

2 votes Thanks 2

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