Tính: làm chi tiết giúp em
`\frac{\sqrt{2}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}“+“\frac{\sqrt{2}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}`
Tính: làm chi tiết giúp em
`\frac{\sqrt{2}}{2\sqrt{2}+\sqrt{3+\sqrt{5}}}“+“\frac{\sqrt{2}}{2\sqrt{2}-\sqrt{3-\sqrt{5}}}`
`sqrt2/(2sqrt2+sqrt{3+sqrt5})+sqrt2/(2sqrt2-sqrt{3-sqrt5})`
`=(sqrt2.sqrt2)/(2sqrt2.sqrt2+sqrt{6+2sqrt5})+(sqrt2.sqrt2)/(2sqrt2.sqrt2-sqrt{6-2sqrt5})`
`=2/(4+sqrt{5+2sqrt5+1})+2/(4-sqrt{5-2sqrt5+1})`
`=2/(4+sqrt{(sqrt5+1)^2}+2/(4-sqrt{(sqrt5-1)^2})`
`=2/(4+sqrt5+1)+2/(4-sqrt5+1)`
`=2/(5+sqrt5)+2/(5-sqrt5)`
`=(2(sqrt5-1))/(sqrt5(sqrt5+1)(sqrt5-1))+(2(sqrt5+1))/(sqrt5(sqrt5-1)(sqrt5-1))`
`=(2(sqrt5-1)+2(sqrt5+1))/(sqrt5(5-1))`
`=(2sqrt5-2+2sqrt5+2)/(4sqrt5)`
`=(4sqrt5)/(4sqrt5)=1`
Đây nhé