Giải phương trình : (2020-x)^3+(2021-x)^3+(2x-4011)^3=0 25/09/2021 Bởi Cora Giải phương trình : (2020-x)^3+(2021-x)^3+(2x-4011)^3=0
Đặt `2020-x=a;2021-x=b` `=>a+b=4041-2x;b=1+a` Pt `<=>a^3+b^3-(a+b)^3=0` `<=>a^3+(1+a)^3-(2a+1)^3=0` `<=>a^3+1+a^3+3a^2+3a-8a^3-12a^2-6a-1=0` `<=>-6a^3-9a^2-3a=0` `<=>-a(6a^2+9a+3)=0` `<=>-a(6a^2+6a+3a+3)=0` `<=>a(2a+1)(a+1)=0` `<=>a in {0;-1;-1/2}` Vs `a=0` `=>x=2020` Vs `a=-1 =>x=2021` Vs `a=-1/2 =>x=2020-0,5=2019,5` Bình luận
Đặt `2020-x=a;2021-x=b`
`=>a+b=4041-2x;b=1+a`
Pt `<=>a^3+b^3-(a+b)^3=0`
`<=>a^3+(1+a)^3-(2a+1)^3=0`
`<=>a^3+1+a^3+3a^2+3a-8a^3-12a^2-6a-1=0`
`<=>-6a^3-9a^2-3a=0`
`<=>-a(6a^2+9a+3)=0`
`<=>-a(6a^2+6a+3a+3)=0`
`<=>a(2a+1)(a+1)=0`
`<=>a in {0;-1;-1/2}`
Vs `a=0` `=>x=2020`
Vs `a=-1 =>x=2021`
Vs `a=-1/2 =>x=2020-0,5=2019,5`