Đáp án:
`S={-1}`
Giải thích các bước giải:
`x^2+4x+5=2sqrt{2x+3}(xge-3/2)`
`<=>2sqrt{2x+3}-x^2-4x-5=0`
`<=>(2sqrt{2x+3}-2)-x^2-4x-3=0`
`<=>((2sqrt{2x+3}-2)(2sqrt{2x+3}+2))/(2sqrt{2x+3}+2)-(x+1)(x+3)=0`
`<=>(4.(2x+3)-4)/(2sqrt{2x+3}+2)-(x+1)(x+3)=0`
`<=>(4.(2x+2))/(2sqrt{2x+3}+2)-(x+1)(x+3)=0`
`<=>(8.(x+1))/(2sqrt{2x+3}+2)-(x+1)(x+3)=0`
`<=>(x+1)[8/(2sqrt{2x+3}+2)-x-3]=0`
TH`1`:
`x+1=0<=>x=-1`
TH`2`:
`8/(2sqrt{2x+3}+2)-x-3=0`
`<=>(8/(2sqrt{2x+3}+2)-2)-(x+1)=0`
`<=>(8-4sqrt{2x+3}-4)/(2sqrt{2x+3}+2)-(x+1)=0`
`<=>(4-4sqrt{2x+3})/(2sqrt{2x+3}+2)-(x+1)=0`
`<=>((4-4sqrt{2x+3})(4+4sqrt{2x+3}))/((2sqrt{2x+3}+2)(4+4sqrt{2x+3}))-(x+1)=0`
`<=>(16-32x-48)/((2sqrt{2x+3}+2)(4+4sqrt{2x+3}))-(x+1)=0`
`<=>(-32.(x+1))/((2sqrt{2x+3}+2)(4+4sqrt{2x+3}))-(x+1)=0`
`<=>(x+1)(-32/((2sqrt{2x+3}+2)(4+4sqrt{2x+3}))-1)=0`
`<=>x=-1` (Do `-32/((2sqrt{2x+3}+2)(4+4sqrt{2x+3}))-1<0forall xge-3/2)`
Vậy `S={-1}`
