Question

x²+3x+1=(x+3)\(\sqrt{x^2+1}\)

Answer 1

`x^2+3x+1=(x+3)sqrt{x^2+1}`
`<=>x(x+3)+1=(x+3)sqrt{x^2+1}`
`<=>(x+3)(sqrt{x^2+1}-x)=1`
`<=>((x+3)(sqrt{x^2+1-x)(sqrt{x^2+1}+x))/(sqrt{x^2+1}+x)=1`
`<=>(x+3)/(sqrt{x^2+1}+x)=1`
`<=>x+3=sqrt{x^2+1}+x`
`<=>sqrt{x^2+1}=3`
`<=>x^2+1=9`
`<=>x^2=8`
`<=>x=+-2sqrt2`
Vậy `S={2sqrt2,-2sqrt2}`

Answer 2

`x^2+3x+1=(x+3)\sqrt(x^2+1)`

`<=> x^4+6x^3+11x^2+6x+1=(x^2+6x+9)(x^2+1)`

`<=> x^4+6x^3+11x^2+6x+1=x^4+6x^3+10x^2+6x+9`

`<=> 11x^2+1=10x^2+9`

`<=> x^2=8`

`<=> x=\pm 2\sqrt2`.

Answer 3

Sửa lại nha lỗi quá '-'

`x^2+3x+1=(x+3)sqrt{x^2+1}`
`<=>x(x+3)+1=(x+3)sqrt{x^2+1}`
`<=>(x+3)(sqrt{x^2+1}-x)=1`
`<=>((x+3)(sqrt{x^2+1}-x)(sqrt{x^2+1}+x))/(sqrt{x^2+1}+x)=1`
`<=>(x+3)/(sqrt{x^2+1}+x)=1`
`<=>x+3=sqrt{x^2+1}+x`
`<=>sqrt{x^2+1}=3`
`<=>x^2+1=9`
`<=>x^2=8`
`<=>x=+-2sqrt2`
Vậy `S={2sqrt2,-2sqrt2}`