Đáp án+Giải thích các bước giải:
`x=1/2\sqrt{(sqrt2-1)/(sqrt2+1)}`
`x=1/2\sqrt{(sqrt2-1)^2/(2-1)}`
`x=1/2*|sqrt2-1|`
`x=(sqrt2-1)/2`
`<=>2x=sqrt2-1`
`<=>2x+1=sqrt2`
`<=>(2x+1)^2=2`
`<=>4x^2+4x-1=0`
`=>(4x^5+4x^4-x^3+1)^19=[x^3(4x^2+4x-1)+1]^19=1`
Ta có:
`(sqrt{4x^5+4x^4-5x^3+5x}+3)^3`
`=(sqrt{4x^5+4x^4-x^3-4x^3-4x^2+x+4x^2+4x-1+1}+3)^3`
`=(sqrt{x^3(4x^2+4x-1)-x(4x^2+4x-1)+4x^2+4x-1+1}+3)^3`
`=(sqrt1+3)^3`
`=4^3=64`
`((1+sqrt2-x)/sqrt{2x^2+2x})^2016`
`=((1+(sqrt2(sqrt2-1))/2)/sqrt{1/2(4x^2+4x-1)+1/2})^2016`
`=((1+(2-sqrt2)/2)/sqrt{1/2})^2016`
`=(((4-sqrt2)/2)/sqrt{1/2})^2016`
`=((4-sqrt2)/sqrt2)^2016`
`=(2sqrt2-1)^2016`
`=>A=1+64+(2sqrt2-1)^2016`
`=>A=65+(2sqrt2-1)^2016`
