Question

Bài 1 : Tính nghiệm :

a) 5x( 2x+7 ) - 3x( 20x - 5 ) + 100

b) x² + 5x - 6

c) x² - 4x + 3

d) 2x² + 5x ⁺ 3

Bài 2 : Chứng minh đa thức sau vô nghiệm :

a) ( x - 1)² + ( x + 5 )²

Answer 1

b) x²+5x-6 =0

\(\Leftrightarrow x^2+6x-x-6=0\)

\(\Leftrightarrow x\left(x+6\right)-\left(x+6\right)=0\)

\(\Leftrightarrow\left(x+6\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+6=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-6\\x=1\end{matrix}\right.\)

Vậy S = {-6;1}

c) x²-4x+3=0

\(\Leftrightarrow x^2-3x-x+3=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

Vậy S = {3;1}

d) 2x²+5x+3=0

\(\Leftrightarrow2x^2+2x+3x+3=0\)

\(\Leftrightarrow2x\left(x+1\right)+3\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\2x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{-3}{2}\end{matrix}\right.\)

Vậy S = {-1;\(\dfrac{-3}{2}\)}

Answer 2

bài 2

\(\left(x-1\right)^2+\left(x+5\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}x-1=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\x=-5\end{matrix}\right.\) (vô lí)

Vậy pt vô nghiệm