Question

 Giải phương trình

a) (x-1)=(x-1)(x-2)

b) Tìm m để phương trình có nghiệm bằng 2

5(x+1)(3x+m)-2.22=56

c) \(\frac{3\left(2x+1\right)}{4}-\frac{5x+3}{6}+\frac{x+1}{2}=x+\frac{7}{12}\)

d) \(\frac{x+1}{2019}+\frac{x+3}{2017}=\frac{x+5}{2015}+\frac{x+7}{2013}\)

Giúp vs

Answer 1

d) x+1/2019 + x+3/2017 = x+5/2015 + x+7/2013

<=> x+1/2019 + x+3/2017 - x+5/2015 - x+7/2013 =0

<=> ( x+1/2019 + 1) + ( x+3/2017 + 1) - ( x+5/2015 + 1) - ( x+7/2013 +1) = 0

<=> ( x+1+2019/2019) +(x+3+2017/2017) - ( x+5+2015/2015) -   ( x+7+2013/2013) =0

<=> x+2020/2019 + x+2020/2017 - x+2020/2015 - x+2020/2013 =0

<=> (x+2020)× ( 1/2019 + 1/2017 - 1/2015 - 1/2013) =0

Mà 1/2019 + 1/2017 - 1/2015 - 1/2013  khác 0

=> x+2020 =0

=> x = -2020

Answer 2

\(\left(x-1\right)=\left(x-1\right)\left(x-2\right)\)

\(\Leftrightarrow\left(x-1\right)-\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\)

HOẶC\(x-1=0\Leftrightarrow x=1\)(NHẬN)

HOẶC\(x-3=0\Leftrightarrow x=3\)(NHẬN)

VẬY: tập ngiệm của pt là S={1;3}

Answer 3

a) (x-1) = (x-1)(x-2)

<=> (x-1) - (x-1)(x+2) =0

<=> (x+1)× [ 1- ( x+2)] =0

<=> (x+1) × ( 1-x-2)=0

<=> (x+1) × (-1-x) =0

TH1:

x+1 =0 => x = -1

TH2:

-1-x =0 => x = -1