Toán Lớp 9: căn54 +căn2 phần căn3 + 1 + 4 phần căn6 + căn2

Question

Toán Lớp 9:  căn54 +căn2 phần căn3 + 1            +           4 phần căn6 + căn2

maianhnhiquynh · Answer

sqrt{54} + ( sqrt{2})/(( sqrt{3}+1) + 4/( sqrt{6}+ sqrt{2})   = sqrt{54} + ( sqrt{2}( sqrt{3}-1))/(( sqrt{3}+1)( sqrt{3}-1)) + [4( sqrt{6}- sqrt{2})]/[( sqrt{6}+ sqrt{2})( sqrt{6}- sqrt{2})]   = 3 sqrt{6} + ( sqrt{2}( sqrt{3}-1))/(3-1) + [4( sqrt{6}- sqrt{2})]/(6-2)   = 3 sqrt{6} + ( sqrt{2}( sqrt{3}-1))/2 + [4( sqrt{6}- sqrt{2})]/4   = 3 sqrt{6} + ( sqrt{2}( sqrt{3}-1))/2 + [4( sqrt{6}- sqrt{2})]/4   = 3 sqrt{6} +  sqrt{6} -  sqrt{2} + ( sqrt{2}( sqrt{3}-1))/2   = 4 sqrt{6} -  sqrt{2} + ( sqrt{2}( sqrt{3}-1))/2   = (8 sqrt{6}-2 sqrt{2})/2 + ( sqrt{2}( sqrt{3}-1))/2   = (8 sqrt{6}-2 sqrt{2}+ sqrt{6}- sqrt{2})/2   = (9 sqrt{6}-3 sqrt{2})/2

thudan · Answer

( sqrt{54}+ sqrt{2})/( sqrt{3}+1)+(4)/( sqrt{6}+ sqrt{2})   =(( sqrt{54}+ sqrt{2})( sqrt{3}-1))/(( sqrt{3}+1)( sqrt{3}-1))+(4( sqrt{6}- sqrt{2}))/(( sqrt{6}+ sqrt{2})( sqrt{6}- sqrt{2}))   =(9 sqrt{2}-3 sqrt{6}+ sqrt{6}- sqrt{2})/(2)+ sqrt{6}- sqrt{2}   =(8 sqrt{2}-2 sqrt{6})/(2)+ sqrt{6}- sqrt{2}   =(2 sqrt{2}(4- sqrt{3}))/(2)+ sqrt{6}- sqrt{2}   = sqrt{2}(4- sqrt{3})+ sqrt{6}- sqrt{2}   =4 sqrt{2}- sqrt{6}+ sqrt{6}- sqrt{2}   =3 sqrt{2}