Question

[Le Xuan Mai]

chứng minh đẳng thức:\(\left(4+\sqrt{15}\right).\left(\sqrt{10}\sqrt{6}\right)\sqrt{4-\sqrt{15}=2}\)

Answer 1

[Akai Haruma]

Lời giải:

$(4+\sqrt{15})(\sqrt{10}-\sqrt{6})\sqrt{4-\sqrt{15}}$

$=(4+\sqrt{15})(\sqrt{5}-\sqrt{3})\sqrt{8-2\sqrt{15}}$

$=(4+\sqrt{15})(\sqrt{5}-\sqrt{3})\sqrt{(\sqrt{5}-\sqrt{3})^2}$

$=(4+\sqrt{15})(\sqrt{5}-\sqrt{3})(\sqrt{5}-\sqrt{3})$

$=(4+\sqrt{15})(8-2\sqrt{15})=2(4+\sqrt{15})(4-\sqrt{15})$

$=2(4^2-15)=2$ (đpcm)