Ta có: `x^2 -5x+ 1 + sqrt(x^4+ 7x^2 +1) =0`
`-> sqrt(x^4 +7x^2+ 1) = 5x- (x^2 +1)`
Với  `5x -x^2- 1 ge 0:`
`x^4+ 7x^2 +1 = (x^2+ 1)^2 - 10x(x^2 +1)+ 25x^2`
`-> x^4 +7x^2+ 1 = x^4+ 27x^2 +1 - 10x(x^2+ 1)`
`-> 10x(x^2 +1)- 20x^2 =0`
`-> 10x(x^2- 2x +1)= 0`
`-> 10x(x -1)^2 =0`
`-> [(x =0 (loại)),(x= 1 (thỏa mãn)):}`
Vậy `x=1`