Question

Bài 1. Giải phương trình

b) (x - 3)(x - 5) = x ^ 2 - 1

c) x ^ 3 + x ^ 3 - x ^ 2 - 1 = 0

Answer 1

 Bài `1:`

`b)`

`(x-3).(x-5)=x^{2}-1`

`<=>x^{2}-5x-3x+15=x^{2}-1`

`<=>x^{2}-8x+15-x^{2}+1=0`

`<=>-8x+16=0`

`<=>-8x=-16`

`<=>x=2`

Vậy `S={2}`

`c)`

`x^{3}+x^{3}-x^{2}-1=0`

`<=>2x^{3}-x^{2}-1=0`

`<=>2x^{3}-2x^{2}+x^{2}-1=0`

`<=>2x^{2}.(x-1)+(x-1).(x+1)=0`

`<=>(x-1).(2x^{2}+x+1)=0`

Ta có:

`2x^{2}+x+1`

`=2.(x^{2}+1/2x+ 1/2)`

`=2.[x^{2}+2.x. 1/4+(1/4)^{2}+7/16]`

`=2.[(x+1/4)^{2}+7/16]`

`=2.(x+1/4)^{2}+7/8`

Ta có:

`(x+1/4)^{2}\ge0AAx`

`=>2.(x+1/4)^{2}\ge0AAx`

`=>2(x+1/4)^{2}+7/8>0AAx`

`=>x-1=0`

`<=>x=1`

Vậy `S={1}`

`@Nae`