Đáp án+Giải thích các bước giải:
`1)`
`a)`
`2x(x-3)+5x-15`
`=2x^2-6x+5x-15`
`=2x^2-x-15`
`b)`
`2x(2x-3)-3+2x`
`=4x^2-6x-3+2x`
`=4x^2-4x-3`
`c)`
`x(3x-5)-6x+10=0`
`<=>3x^2-5x-6x+10=0`
`<=>3x^2-11x+10=0`
`<=>3x^2-6x-5x+10=0`
`<=>(3x^2-6x)-(5x-10)=0`
`<=>3x(x-2)-5(x-2)=0`
`<=>(x-2)(3x-5)=0`
`<=>[(x-2=0),(3x-5=0):}`
`<=>[(x=2),(3x=5):}`
`<=>[(x=2),(x=5/3):}`
Vậy `S={2;5/3}`
`d)`
`3x^2+2x-1=0`
`<=>3x^2+3x-x-1=0`
`<=>(3x^2+3x)-(x+1)=0`
`<=>3x(x+1)-(x+1)=0`
`<=>(x+1)(3x-1)=0`
`<=>[(x+1=0),(3x-1=0):}`
`<=>[(x=-1),(3x=1):}`
`<=>[(x=-1),(x=1/3):}`
Vậy `S={-1;1/3}`
`e)`
`x^2+6x-16=0`
`<=>x^2+8x-2x-16=0`
`<=>(x^2+8x)-(2x+16)=0`
`<=>x(x+8)-2(x+8)=0`
`<=>(x+8)(x-2):=0`
`<=>[(x+8=0),(x-2=0):}`
`<=>[(x=-8),(x=2):}`
Vậy `S={-8;2}`
`f)`
`(2x+5)^2-(x+2)^2=0`
`<=>[(2x+5)-(x+2)][(2x+5)+(x+2)]=0`
`<=>(2x+5-x-2)(2x+5+x+2)=0`
`<=>(x+3)(3x+7)=0`
`<=>[(x+3=0),(3x+7=0):}`
`<=>[(x=-3),(3x=-7):}`
`<=>[(x=-3),(x=-7/3):}`
Vậy `S={-3;-7/3}`
`g)`
`(x-2)(x+1)-x^2+4=0`
`<=>(x-2)(x+1)-(x^2-4)=0`
`<=>(x-2)(x+1)-(x-2)(x+2)=0`
`<=>(x-2)[(x+1)-(x+2)]=0`
`<=>(x-2)(x+1-x-2)=0`
`<=>(x-2).(-1)=0`
`<=>x-2=0`
`<=>x=2`
Vậy `S={2}`
`h)`
`(x^2-4)-(x-2)(3-2x)=0`
`<=>(x-2)(x+2)-(x-2)(3-2x)=0`
`<=>(x-2)[(x+2)-(3-2x)]=0`
`<=>(x-2)(x+2-3+2x)=0`
`<=>(x-2)(3x-1)=0`
`<=>[(x-2=0),(3x-1=0):}`
`<=>[(x=2),(3x=1):}`
`<=>[(x=2),(x=1/3):}`
Vậy `S={2;1/3}`
`i)`
`(5x-3)^2=(4x-7)^2`
`<=>(5x-3)^2-(4x-7)^2=0`
`<=>[(5x-3)-(4x-7)][(5x-3)+(4x-7)]=0`
`<=>(5x-3-4x+7)(5x-3+4x-7)=0`
`<=>(x+4)(9x-10)=0`
`<=>[(x+4=0),(9x-10=0):}`
`<=>[(x=-4),(9x=10):}`
`<=>[(x=-4),(x=10/9):}`
Vậy `S={-4;10/9}`
`#ld`
