Toán Lớp 9: rút gọn biểu thức
\sqrt{19+6\sqrt{2}}-\sqrt{19-6\sqrt{2}}
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Toán Lớp 9: rút gọn biểu thức
\sqrt{19+6\sqrt{2}}-\sqrt{19-6\sqrt{2}}
Comments ( 2 )
=\sqrt{18+1+6\sqrt{2}}-\sqrt{18+1-6\sqrt{2}}
=\sqrt{(3\sqrt{2})^2+1+2.3\sqrt{2}}-\sqrt{(3\sqrt{2})^2+1-6\sqrt{2}}
=\sqrt{(3\sqrt{2}+1)^2}-\sqrt{(3\sqrt{2}-1)^2}
=|3\sqrt{2}+1|-|3\sqrt{2}-1|
=3\sqrt{2}+1-3\sqrt{2}+1
=2
$=>A^2=19+6\sqrt[]{2}+19-6\sqrt[]{2}-2\sqrt[]{(19+6\sqrt[]{2})(19-6\sqrt[]{2})}$
$=38-2\sqrt[]{19^2-(6\sqrt[]{2})^2}$
$=38-2\sqrt[]{361-72}$
$=38-2\sqrt[]{289}$
$=38-2.17$
$=38-34=4$
$=>A =\sqrt[]{4}=2$