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a. x ( x + 4 ) ( 4 - x ) + ( x - 5 ) ( x2 + 5x + 25 ) = 3
- x ( x + 4 ) ( x - 4) + x3 - 53 = 3
-x . (x2 - 42) + x3 -125 = 3
-x3 + 16x + x3 - 125 = 3
16x - 125 = 3
16x = 128
x =8
a: \(\Leftrightarrow4x^2+4x+1-4x^2-16x-16=9\)
=>-12x-15=9
=>-12x=24
hay x=-2
b: \(\Leftrightarrow9x^2-6x+1+2x^2+12x+18+11\left(1-x^2\right)=6\)
\(\Leftrightarrow11x^2+6x+19+11-11x^2=6\)
=>6x+30=6
=>6x=-24
hay x=-4
c: \(\Leftrightarrow x^3+3x^2+3x+1-x^3-3x^2=2\)
=>3x=1
hay x=1/3
d: \(\Leftrightarrow x^3-6x^2+12x-8-x\left(x^2-1\right)+6x^2=5\)
\(\Leftrightarrow x^3+12x-8-x^3+x=5\)
=>13x=13
hay x=1
e: \(\Leftrightarrow x^3-27-x^3+16x=5\)
=>16x=32
hay x=2
Bài 1:
a) \(9\left(4x+3\right)^2=16\left(3x-5\right)^2\)
\(114x^2+216x+81=114x^2-480x+400\)
\(144x^2+216x=144x^2-480x+400-81\)
\(114x^2+216=114x^2-480x+319\)
\(696x=319\)
\(\Rightarrow x=\frac{11}{24}\)
b) \(\left(x^3-x^2\right)^2-4x^2+8x-4=0\)
\(\left(x-1\right)^2\left(x^2+2\right)\left(x+\sqrt{2}\right)\left(x-\sqrt{2}\right)=0\)
\(\Rightarrow x=1\)
c) \(x^5+x^4+x^3+x^2+x+1=0\)
\(\left(x+1\right)\left(x^2+x+1\right)\left(x^2-x+1\right)=0\)
\(\Rightarrow x=-1\)
Bài 2:
a) \(5x^3-7x^2-15x+21=0\)
\(\left(5x-7\right)\left(x+\sqrt{3}\right)\left(x-\sqrt{3}\right)=0\)
\(\Rightarrow x=\frac{7}{5}\)
b) \(\left(x-3\right)^2=4x^2-20x+25\)
\(x^2-6x+9-25=4x^2-20x+25\)
\(x^2-6x+9=4x^2-20x+25-25\)
\(x^2-6x-16=4x^2-20x\)
\(x^2+14x-16=4x^2-4x^2\)
\(-3x^2+14x-16=0\)
\(\Rightarrow\orbr{\begin{cases}x=2\\x=\frac{8}{3}\end{cases}}\)
c) \(\left(x-1\right)^2-5=\left(x+2\right)\left(x-2\right)-x\left(x-1\right)\)
\(x^2-2x=x-4\)
\(x^2-2x=x-4+4\)
\(x^2-2x=x-x\)
\(x^2-3x=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=3\end{cases}}\)
d) \(\left(2x-3\right)^3-\left(2x+3\right)\left(4x^2-1\right)=-24\)
\(-48x^2+56x-24=-24\)
\(-48x^2+56x=-24+24\)
\(-48x^2+56=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{7}{6}\end{cases}}\)
mình ko chắc
giải
a)(x+2)^2+(x-3)^2-2(x-1)(x+1)
x^2+4x+4+x^2-6x+9-2(x^2-1)=9
x^2+4x+4+x^2-6x+9-2x^2+2=9
-2x+15=9
-2x=9-15
-2x=-6
x=-6:(-2)
x=3
d)4(x+1)^2+(2x-1)^2-8(x-1)(x+1)=11
4(x^2+2x+1)+4x^2+4x+1-8(x^2-1)
4x^2+8x+4+4x^2+4x+1-8x^2+8=11
12x+13=11
12x=11-13
12x=-2
x=-1/6
a)\(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6.\)
\(\Leftrightarrow x^2-4x+4-x^2+9-6=0\)
\(\Leftrightarrow-4x+7=0\)
\(\Leftrightarrow4x=7\Leftrightarrow x=1,75\)
\(b,4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10.\)
\(\Leftrightarrow4\left(x^2-6x+9\right)-4x^2+1-10=0\)
\(\Leftrightarrow-24x+27=0\)
\(\Leftrightarrow24x=27\Leftrightarrow x=1,125\)
2.
a) \(x.\left(x^2+x+1\right)-x^2.\left(x+1\right)-x+5\)
\(\Rightarrow x^3+x^2+x-x^3-x^2-x+5\)
\(\Rightarrow\left(x^3-x^3\right)+\left(x^2-x^2\right)+\left(x-x\right)+5\)
\(=5\)( vì kết quả bằng 5 nên đa thức không phụ thuộc vào biến )
b) \(x.\left(2x+1\right)-x^2.\left(x+2\right)+x^3-x+3\)
\(\Rightarrow2x^2+x-x^3-2x^2+x^3-x+3\)
\(\Rightarrow\left(2x^2-2x^2\right)+\left(x-x\right)+\left(-x^3+x^3\right)+3\)
\(=3\)( vì kết quả bằng 3 nên đa thức không phụ thuộc vào biến )
c) \(4.\left(6+x\right)+x^2.\left(2+3x\right)-x.\left(5x+4\right)+3x^2.\left(1-x\right)\)
\(\Rightarrow24+4x+2x^2+3x^3-5x^2+4x+3x^2-3x^3\)
\(\Rightarrow24+\left(4x-4x\right)+\left(2x^2-5x^2+3x^2\right)+\left(3x^3-3x^3\right)\)
\(=24\)( vì kết quả bằng 24 nên đa thức không phụ thuộc vào biến )
a) \(4x^3-9x=0\)
\(\Leftrightarrow x\left(4x^2-9\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\4x^2=9\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm\frac{3}{2}\end{cases}}\)
b) \(3x\left(x-2\right)-5x+10=0\)
\(\Leftrightarrow\left(3x-5\right)\left(x-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{3}\\x=2\end{cases}}\)
c) \(4x\left(x+3\right)-x^2+9=0\)
\(\Leftrightarrow4x\left(x+3\right)-\left(x-3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left(3x+3\right)\left(x+3\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-3\end{cases}}\)
d) \(\left(2x+5\right)\left(x-4\right)=\left(x-4\right)\left(5-x\right)\)
\(\Leftrightarrow\left(2x+5\right)\left(x-4\right)+\left(x-5\right)\left(x-4\right)=0\)
\(\Leftrightarrow3x\left(x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=4\end{cases}}\)
e) \(16x^2-25=\left(4x-5\right)\left(2x+1\right)\)
\(\Leftrightarrow\left(4x-5\right)\left(4x+5\right)-\left(4x-5\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left(4x-5\right)\left(2x+4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{4}\\x=-2\end{cases}}\)
f) \(\left(x+\frac{1}{5}\right)^2=\frac{64}{9}\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{5}=\frac{8}{3}\\x+\frac{1}{5}=-\frac{8}{3}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{37}{15}\\x=-\frac{43}{15}\end{cases}}\)
g) \(9\left(x+2\right)^2=\left(x+3\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}3x+6=x+3\\3x+6=-x-3\end{cases}}\Leftrightarrow\orbr{\begin{cases}2x=-3\\4x=-9\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{3}{2}\\x=-\frac{9}{4}\end{cases}}\)
k bít làm bl làm j
cho vui