Toán x + 1 / x^2 + x + 1 – x – 1 / x^2 – x + 1 = 3 / x . ( x ^4 + x^2 + 1 ) 20/10/2021 By Emery x + 1 / x^2 + x + 1 – x – 1 / x^2 – x + 1 = 3 / x . ( x ^4 + x^2 + 1 )
Đáp án: `S={3/2}` Giải thích các bước giải: `x^4+x^2+1` `=x^4+2x^2+1-x^2` `=(x^2+1)^2-x^2` `=(x^2-x+1)(x^2+x+1)` `pt<=>(x+1)/(x^2+x+1)-(x-1)/(x^2-x+1)=3/(x(x^2-x+1)(x^2+x+1))(x ne +-1)` `<=>x(x+1)(x^2-x+1)-x(x-1)(x^2+x+1)=3` `<=>x(x^3+1)-x(x^3-1)=3` `<=>2x=3` `<=>x=3/2` Vậy `S={3/2}` Trả lời
Đáp án:
`S={3/2}`
Giải thích các bước giải:
`x^4+x^2+1`
`=x^4+2x^2+1-x^2`
`=(x^2+1)^2-x^2`
`=(x^2-x+1)(x^2+x+1)`
`pt<=>(x+1)/(x^2+x+1)-(x-1)/(x^2-x+1)=3/(x(x^2-x+1)(x^2+x+1))(x ne +-1)`
`<=>x(x+1)(x^2-x+1)-x(x-1)(x^2+x+1)=3`
`<=>x(x^3+1)-x(x^3-1)=3`
`<=>2x=3`
`<=>x=3/2`
Vậy `S={3/2}`