a) Ta có: A = 0
=> x2 + 2x - 3 = 0
=> x2 + 3x - x - 3 = 0
=> x(x + 3) - (x + 3) = 0
=> (x - 1)(x + 3) = 0
=> \(\orbr{\begin{cases}x-1=0\\x+3=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x=-3\end{cases}}\)
Vậy ...
b) Ta có: B = 0
=> -3x2 + 12x - 9 = 0
=> -3x2 + 3x + 9x - 9 = 0
=> -3x(x - 1) + 9(x - 1) = 0
=> (-3x + 9)(x - 1) = 0
=> -3(x - 3)(x - 1) = 0
=> (x - 3)(x - 1) = 0
=> \(\orbr{\begin{cases}x-3=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
Vậy ...
c) C = 0
=> 10x2 - 7x - 3 = 0
=> 10x2 - 10x + 3x - 3 = 0
=> 10x(x - 1) + 3(x - 1) = 0
=> (10x + 3)(x - 1) = 0
=> \(\orbr{\begin{cases}10x+3=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}10x=-3\\x=1\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{3}{10}\\x=1\end{cases}}\)
d) D = 0
=> -7x4 + 10x3 - 3x2 = 0
=> x2(-7x2 + 10x - 3) = 0
=> x2(-7x2 + 7x + 3x - 3) = 0
=> x2.[-7x(x - 1) + 3(x - 1)] = 0
=> x2.(-7x + 3)(x - 1) = 0
=> x^2 = 0
-7x + 3 = 0
hoặc x - 1 = 0
=> x= 0
-7x = -3
hoặc x = 1
=> x = 0
hoặc x = 3/7
hoặc x = 1
Vậy ...
a) \(A=x^2+2x-3\)
\(x^2+2x-3=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x+3=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=1\\x=-3\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=1\\x=-3\end{cases}}\)
b) \(B=-3x^2+12x-9\)
\(-3x^2+12x-9=0\)
\(\Leftrightarrow-3\left(x^2-4x+3\right)=0\)
\(\Leftrightarrow-3\left(x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x-3=0\\x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
c) \(C=10x^2-7x-3\)
\(10x^2-7x-3=0\)
\(\Leftrightarrow x\left(10x+3\right)-\left(10x+3\right)=0\)
\(\Leftrightarrow\left(10x+3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}10x+3=0\\x-1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{10}\\x=1\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-\frac{3}{10}\\x=1\end{cases}}\)
d) \(D=-7x^4+10x^3-3x^2\)
\(-7x^4+10x^3-3x^2=0\)
\(\Leftrightarrow-x^2\left(7x^2-10x+3\right)=0\)
\(\Leftrightarrow-x^2\left(7x^2-3x-7x+3\right)=0\)
\(\Leftrightarrow-x^2\left[x\left(7x-3\right)-\left(7x-3\right)\right]=0\)
\(\Leftrightarrow-x^2\left(7x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow x^2\left(7x-3\right)\left(x-1\right)=0\)
\(\Leftrightarrow\hept{\begin{cases}x^2=0\\7x-3=0\\x-1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=0\\x=\frac{3}{7}\\x=1\end{cases}}\)(thay ngoặc nhọn bằng ngoặc vuông nhé, phần kl cũng thay luôn như thế nhé)
\(\Rightarrow\hept{\begin{cases}x=0\\x=\frac{3}{7}\\x=1\end{cases}}\)
