Question

b1: giải các pt sau:
a)(2x-1)²=4x(x-1)
b) l 3x-1 l = l -5 l
c)x+1/x-1 - x-1/x+1=16/x²-1

Answer 1

a)<=>\(4x^2-4x+1=4x_2-4x\)

<=>\(4x^2-4x-4x^2+4x=-1\)

<=>\(0x=1\)

vô nghiệm

b)l3x-1l=l-5l

<=>l3xl=l-5-1l

<=>l3xl=l-6l

<=>lxl=l\(\dfrac{-6}{3}\)l

<=>lxl=l-2l

<=>x=2

c)\(\dfrac{x-1}{x+1}-\dfrac{x-1}{x+1}=\dfrac{16}{x^2-1}\)

ĐKXĐ:\(x\ne\mp1\)

\(\dfrac{x-1}{x+1}-\dfrac{x+1}{x-1}=\dfrac{16}{x^2-1}\)

\(\dfrac{\left(x+1\right)\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}-\dfrac{\left(x-1\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}=\dfrac{16}{\left(x+1\right)\left(x-1\right)}\)

=>\(\left(x+1\right)\left(x+1\right)-\left(x-1\right)\left(x-1\right)=16\)

<=>\(x^2+x+x+1-x^2+x+x-1=16\)

<=>\(x^2+x+x-x^2+x+x=16-1+1\)

<=>\(4x=16\)

<=>x=4(TM)