Đáp án:
`a)A=1/(sqrt1+sqrt2)+1/(sqrt2+sqrt3)+.....+1/(sqrt{24}+sqrt{25})`
`=(sqrt2-sqrt1)/(2-1)+(sqrt3-sqrt2)/(3-2)+.....+(sqrt{25}-sqrt{24})/(25-24)`
`=sqrt2-1+sqrt3-sqrt2+.....+sqrt{25}-sqrt{24}`
`=sqrt{25}-1`
`=5-1=4`
`b)(\sqrt{1/(sqrt1+sqrt2)+1/(sqrt2+sqrt3)+.....+1/(sqrt{2024}+sqrt{2025})}).x=22`
`<=>(\sqrt{(sqrt2-sqrt1)/(2-1)+(sqrt3-sqrt2)/(3-2)+.....+(sqrt{2025}-sqrt{2024})/(2025-2024)}).x=22`
`<=>(\sqrt{sqrt2-sqrt1+sqrt3-sqrt2+.....+sqrt{2025}-sqrt{2024}}).x=22`
`<=>(sqrt{\sqrt{2025]-1}).x=22`
`<=>sqrt{45-1}.x=22`
`<=>sqrt{44}.x=22`
`<=>x=22/sqrt{44}=\sqrt{11}`.
Vậy phương trình có nghiệm `S={\sqrt{11}}`.
