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Bài 5 :
f, bạn xem lại đề hay là tìm x chứa tham số a ?
g, \(x^2+3x-\left(2x+6\right)=0\Leftrightarrow x\left(x+3\right)-2\left(x+3\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\Leftrightarrow x=-3;x=2\)
h, \(5x+20-x^2-4x=0\Leftrightarrow5\left(x+4\right)-x\left(x+4\right)=0\)
\(\Leftrightarrow\left(5-x\right)\left(x+4\right)=0\Leftrightarrow x=-4;x=5\)
m, \(x^3-5x^2-x+5=0\Leftrightarrow x^2\left(x-5\right)-\left(x-5\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-5\right)=0\Leftrightarrow x=\pm1;x=5\)
n, \(x\left(x-3\right)-7x+21=0\Leftrightarrow x\left(x-3\right)-7\left(x-3\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left(x-3\right)=0\Leftrightarrow x=3;x=7\)
`Answer:`
a, `4x^2-24x+36=(x-3)^3`
`<=>4(x^2-6x+9)-(x-3)^3=0`
`<=>4(x-3)^2-(x-3)^3=0`
`<=>(x-3)^2.(4-x+3)=0`
`<=>(x-3)^2.(7-x)=0`
`<=>x-3=0` hoặc `7-x=0`
`<=>x=3` hoặc `x=7`
b, `(8x^3-7x^2):x^2=3x+\sqrt{\frac{9}{25}}`
`<=>8x^3:x^2-7x^2:x^2=3x+\sqrt{\frac{9}{25}}`
`<=>8x-7=3x+\sqrt{\frac{9}{25}}`
`<=>8x-7=3x+3/5`
`<=>8x=3x+\frac{38}{5}`
`<=>8x-3x=3x+\frac{38}{5}-3x`
`<=>5x=\frac{38}{5}`
`<=>x=\frac{38}{25}`
a) x2 - 4x - 5 = 0
=> x2 - 5x + x - 5 = 0
=> x(x - 5) + (x - 5) = 0
=> (x + 1)(x - 5) = 0
=> \(\orbr{\begin{cases}x+1=0\\x-5=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=-1\\x=5\end{cases}}\)
b) 4x2 + 7x - 11 = 0
=> 4x2 + 11x - 4x - 11 = 0
=> x(4x + 11) - (4x + 11) = 0
=> (x - 1)(4x + 11) = 0
=> \(\orbr{\begin{cases}x-1=0\\4x+11=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=1\\x=-\frac{11}{4}\end{cases}}\)
c) -7x2 + 6x + 1 = 0
=> -7x2 + 7x - x + 1 = 0
=> -7x(x - 1) - (x - 1) = 0
=> (-7x - 1)(x - 1) = 0
=> \(\orbr{\begin{cases}-7x-1=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}-7x=1\\x=1\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{1}{7}\\x=1\end{cases}}\)
d) -10x2 + 7x + 3 = 0
=> -10x2 + 10x - 3x + 3 = 0
=> -10x(x - 1) - 3(x - 1) = 0
=> (-10x - 3)(x - 1) = 0
=> \(\orbr{\begin{cases}-10x-3=0\\x-1=0\end{cases}}\)
=> \(\orbr{\begin{cases}-10x=3\\x=1\end{cases}}\)
=> \(\orbr{\begin{cases}x=-\frac{3}{10}\\x=1\end{cases}}\)
1 x mũ 2 + 4xy + 4y mũ 2 = x^2 + 4xy + 4y^2 =(2y+x)^2
2, 4x mũ 2 - 36y mũ 2 =4x^2 -36y^2 = -4 (3y-x) (3y+x)
\(7x.\left(x-2\right)-5.\left(x-1\right)=7x^2+3\)
\(7x^2-14x-5x+5=7x^2+3\)
\(7x^2-19x+5=7x^2+3\)
\(7x^2-19x+5-\left(7x^2+3\right)=0\)
\(7x^2-19x+5-7x^2-3=0\)
\(-19x+2=0\)
\(-19x=0-2\)
\(-19x=-2\)
\(x=\frac{2}{19}\)