Đáp án:
a) \(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)
b) \(\left[ \begin{array}{l}x=\dfrac{3}{2}\\x=-1\end{array} \right.\)
c) \(\left[ \begin{array}{l}x=3\\x=-1\end{array} \right.\)
d) \(\left[ \begin{array}{l}x=-3\\x=\dfrac{1}{2}\end{array} \right.\)
Giải thích các bước giải:
a) `(x-5)^2-4x(5-x)=0`
`->(5-x)^2-4x(5-x)=0`
`-> (5-x)(5-x-4x)=0`
`-> (5-x)(5-5x)=0`
`->(5-x)(1-x)=0`
`->`\(\left[ \begin{array}{l}5-x=0\\1-x=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)
b) `(4x-1)^2=25`
`->(4x-1)^2-5^2=0`
`-> (4x-1-5)(4x-1+5)=0`
`-> (4x-6)(4x+4)=0`
`->(2x-3)(x+1)=0`
`->` \(\left[ \begin{array}{l}2x-3=0\\x+1=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=\dfrac{3}{2}\\x=-1\end{array} \right.\)
c)
`x^2-2x=3`
`->x^2-2x+1-4=0`
`->(x-1)^2-2^2=0`
`->(x-1-2)(x-1+2)=0`
`->(x-3)(x+1)=0`
`->` \(\left[ \begin{array}{l}x-3=0\\x+1=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=3\\x=-1\end{array} \right.\)
d)
`2x^2+5x=3`
`->2x^2+5x-3=0`
`->2x^2-x+6x-3=0`
`->x(2x-1)+3(2x-1)=0`
`->(x+3)(2x-1)=0`
`->`\(\left[ \begin{array}{l}x+3=0\\2x-1=0\end{array} \right.\)
`->` \(\left[ \begin{array}{l}x=-3\\x=\dfrac{1}{2}\end{array} \right.\)
