Toán Lớp 9: Giúp vs mn hứa cho 5* + CTLHN
Thực hiện phép tính:
$\sqrt{3+\sqrt{5}}$ + $\sqrt{7-3\sqrt{5}}$ – $\sqrt{2}$
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Toán Lớp 9: Giúp vs mn hứa cho 5* + CTLHN
Thực hiện phép tính:
$\sqrt{3+\sqrt{5}}$ + $\sqrt{7-3\sqrt{5}}$ – $\sqrt{2}$
Comments ( 2 )
=sqrt{(2.(3+sqrt{5}))/2}+sqrt{(2.(7-3sqrt{5}))/2}-sqrt{2}
=sqrt{(6+2sqrt{5})/2}+sqrt{(14-6sqrt{5})/2}-sqrt{2}
=sqrt{6+2sqrt{5}}/sqrt{2}+sqrt{14-6sqrt{5}}/sqrt{2}-sqrt{2}
=sqrt{(sqrt{5})^2+2.sqrt{5}.1+1^2}/sqrt{2}+sqrt{3^2-2.3.sqrt{5}+(sqrt{5})^2}/sqrt{2}-sqrt{2}
=sqrt{(sqrt{5}+1)^2}/sqrt{2}+sqrt{(3-sqrt{5})^2}/sqrt{2}-sqrt{2}
=|sqrt{5}+1|/sqrt{2}+|3-sqrt{5}|/sqrt{2}-sqrt{2}
=(sqrt{5}+1)/sqrt{2}+(3-sqrt{5})/sqrt{2}-sqrt{2} ( vì sqrt{9}(=3)>sqrt{5})
=(sqrt{5}+1+3-sqrt{5})/sqrt{2}-sqrt{2}
=(4)/sqrt{2}-sqrt{2}
=(sqrt{2}.sqrt{2}.2)/sqrt{2}-sqrt{2}
=2sqrt{2}-sqrt{2}
=sqrt{2}