Đáp án+Giải thích các bước giải:
d) `(3/(sqrt{5}-sqrt{2))+4/(sqrt{6}+sqrt{2}))` `.` `(sqrt{3}-1)^2`
`=` `((5-2)/(sqrt{5}-sqrt{2})+(6-2)/(sqrt{6}+sqrt{2}))` $.$ `(3-2sqrt{3}+1)`
`=` `[((sqrt{5}-sqrt{2})(sqrt{5}+sqrt{2}))/(sqrt{5}-sqrt2)` `+` `((sqrt{6}-sqrt{2})(sqrt{6}+sqrt{2}))/(sqrt{6}+sqrt{2})]` `.` `(4-2sqrt{3})`
`=` `(sqrt{5}+sqrt{2}+sqrt{6}-sqrt{2}).(4-2sqrt{3})`
`=` `(sqrt{5}+sqrt6).(4-2sqrt{3})`
e) `1/(1+sqrt2)+1/(sqrt2+sqrt3)+....+1/(sqrt99+sqrt100`
`=` `(2-1)/(1+sqrt2)+(3-2)/(sqrt2+sqrt3)+.......+(100-99)/(sqrt99+sqrt100`
`=` `((sqrt2-sqrt1)(sqrt2+sqrt1))/(1+sqrt2)+((sqrt3-sqrt2)(sqrt3+sqrt2))/(sqrt2+sqrt3)+......+((sqrt100-sqrt99)(sqrt100+sqrt99))/(sqrt99+sqrt100`
`=` `sqrt2-sqrt1+sqrt3-sqrt2+....+sqrt100-sqrt99`
`=` `-sqrt1+sqrt100`
`=` `-1+10`
`=` `9`