Đáp án + Giải thích các bước giải:
Bài `5` :
`a)` `16x^2-(4x+5)^2=15`
`<=>(4x)^2-(4x+5)^2=15`
`<=>[4x-(4x+5)][4x+(4x+5)]=15`
`<=>(4x-4x-5)(4x+4x+5)=15`
`<=>-5(8x+5)=15`
`<=>8x+5=-3`
`<=>8x=-8`
`<=>x=-1`
Vậy `S={-1}`
`b)` `(2x+3)^2-4(x-1)(x+1)=49`
`<=>4x^2+12x+9-4(x^2-1)=49`
`<=>4x^2+12x+9-4x^2+4=49`
`<=>12x+13=49`
`<=>12x=36`
`<=>x=3`
Vậy `S={3}`
`c)` `(2x+1)(1-2x)+(1-2x)^2=18`
`<=>(1-2x)[(2x+1)+(1-2x)]=18`
`<=>(1-2x)(2x+1+1-2x)=18`
`<=>(1-2x)*2=18`
`<=>1-2x=9`
`<=>2x=-8`
`<=>x=-4`
Vậy `S={-4}`
`d)` `2(x+1)^2-(x-3)(x+3)-(x-4)^2=0`
`<=>2(x^2+2x+1)-(x^2-9)-(x^2-8x+16)=0`
`<=>2x^2+4x+2-x^2+9-x^2+8x-16=0`
`<=>12x-5=0`
`<=>x=5/12`
Vậy `S={5/12}`
`e)` `(x-5)^2-x(x-4)=9`
`<=>x^2-10x+25-x^2+4x=9`
`<=>-6x=-16`
`<=>x=16/6=8/3`
Vậy `S={8/3}`
`f)` `(x-5)^2+(x-4)(1-x)=0`
`<=>x^2-10x+25+(x-x^2-4+4x)=0`
`<=>x^2-10x+25+x-x^2-4+4x=0`
`<=>-5x+21=0`
`<=>5x=-21`
`<=>x=21/5`
Vậy `S={21/5}`.
