Giải phương trình:
a,(2x-1) cộng(x-3).(2x-1) bằng 0
b,2(x-5).(x cộng 2) bằng x^2 – 5x
c,(2x cộng 1).(1-x) cộng 2x bằng 2
d,x^2 – 5x cộng 6 bằng 0
Giúp mình với!!Gấp
Giải phương trình:
a,(2x-1) cộng(x-3).(2x-1) bằng 0
b,2(x-5).(x cộng 2) bằng x^2 – 5x
c,(2x cộng 1).(1-x) cộng 2x bằng 2
d,x^2 – 5x cộng 6 bằng 0
Giúp mình với!!Gấp
Đáp án:
Giải thích các bước giải:
\(\begin{array}{l}
a.(2x – 1) + (x – 3)(2x – 1) = (2x – 1)(x – 3 + 1) = 0\\
\to \left[ \begin{array}{l}
x = \frac{1}{2}\\
x = 2
\end{array} \right.\\
b.2(x – 5)(x + 2) = x(x – 5)\\
\to (x – 5)(2x + 4 – x) = 0\\
\to \left[ \begin{array}{l}
x = 5\\
x = – 4
\end{array} \right.\\
c.(2x + 1)(1 – x) + 2x = 2\\
\to 2x – 2{x^2} + 1 – x + 2x – 2 = 0\\
\to (x – 1)(2x – 1) = 0\\
\to \left[ \begin{array}{l}
x = 1\\
x = \frac{1}{2}
\end{array} \right.\\
d.{x^2} – 5x + 6 = 0\\
\to (x – 3)(x – 2) = 0\\
\to \left[ \begin{array}{l}
x = 3\\
x = 2
\end{array} \right.
\end{array}\)
a, ( 2x-1) + ( x-3).( 2x-1)= 0
⇔ ( 2x-1).( x-3+1)= 0
⇔ ( 2x-1).( x-2)= 0
⇔ \(\left[ \begin{array}{l}2x-1=0\\x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=0,5\\x=2\end{array} \right.\)
b, 2( x-5).( x + 2)= x² – 5x
⇔ 2( x-5).( x + 2)= x.( x-5)
⇔ ( x-5).( 2x+4-x) = 0
⇔ ( x-5).( x+4)=0
⇔ \(\left[ \begin{array}{l}x-5=0\\x+4=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=5\\x=-4\end{array} \right.\)
c, ( 2x+1).( 1-x)+2x=2
⇔ ( 2x+1).( 1-x)+2x-2=0
⇔ ( 2x+1).( 1-x)+2.( x-1)=0
⇔ ( x-1).( -2x-1+2)=0
⇔ ( x-1).( -2x+1)
⇔ \(\left[ \begin{array}{l}x-1=0\\-2x+1=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1\\x=0,5\end{array} \right.\)
d, x²-5x+6=0
⇔ x²-3x-2x+6=0
⇔ x.( x-3)-2.( x-3)=0
⇔ ( x-3).( x-2)= 0
⇔ \(\left[ \begin{array}{l}x-3=0\\x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=3\\x=2\end{array} \right.\)