3a+1/3 x √27/9 1+ 3a)^2 với a > -1/3
rút gọn zùm mình với
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8x3+36x2+54x+27
tại x =-4
=>8×(-4)3+36×(-4)2+54×(-4)+27
=8×(-64)+36×16+54×(-4)+27
=-512+576-216+27
=-125
(4x-3)(16x2+12x+9)-x2(64x-4)
=4x(16x2+12x+9)- 3(16x2+12x+9)-x2(64x-4)
=(64x3+48x2+36x)-(48x2+36x+27)-(64x3-4x2)
=64x3+48x2+36x-48x2-36x-27-64x3+4x2
=(64x3-64x3)+(48x2-48x2+4x2)+(36x-36x)-27
=4x2-27
tại x=-1/4
=> 4×(-1/4)2-27
=4×1/16-27
=1/4-27
=-107/4
(ko bt cs đúng ko nx )
\(\frac{x^4-x^3-x+1}{x^4+x^3+3x^2+2x+2}\)
\(=\frac{x^3\left(x-1\right)-\left(x-1\right)}{x^4+x^3+x^2+2x^2+2x+2}\)
\(=\frac{\left(x-1\right)\left(x^3-1\right)}{x^2\left(x^2+x+1\right)+2\left(x^2+x+1\right)}\)
\(=\frac{\left(x-1\right)\left(x-1\right)\left(x^2+x+1\right)}{\left(x^2+x+1\right)\left(x^2+2\right)}\)
\(=\frac{\left(x-1\right)^2}{\left(x^2+2\right)}\)
\(\left(\frac{3a+1}{a^2-3a}+\frac{3a-1}{a^2+3a}\right)\):\(\frac{a^2+1}{a^2-9}\)
=\(\left[\frac{3a+1}{a\left(a-3\right)}+\frac{3a-1}{a\left(a+3\right)}\right]\): \(\frac{a^2+1}{\left(a-3\right)\left(a+3\right)}\)
=\(\left[\frac{\left(3a+1\right)\left(a+3\right)}{a\left(a-3\right)\left(a+3\right)}+\frac{\left(3a-1\right)\left(a-3\right)}{a\left(a+3\right)\left(a-3\right)}\right]\): \(\frac{a^2+1}{\left(a-3\right)\left(a+3\right)}\)
=\(\frac{3a^2+9a+a+3+3a^2-9a-a+3}{a\left(a-3\right)\left(a+3\right)}\): \(\frac{a^2+1}{\left(a-3\right)\left(a+3\right)}\)
=\(\frac{6a^2+6}{a\left(a-3\right)\left(a+3\right)}\): \(\frac{a^2+1}{\left(a-3\right)\left(a+3\right)}\)
=\(\frac{6\left(a^2+1\right)}{a\left(a-3\right)\left(a+3\right)}\).\(\frac{\left(a-3\right)\left(a+3\right)}{a^2+1}\)
=\(\frac{6}{a}\)
`Q=(a^3-3a^2+3a-1)/(a^2-1)`
`a)ĐK:a^2-1 ne 0<=>a ne +-1`
`Q=(a^3-3a^2+3a-1)/(a^2-1)`
`=(a-1)^3/((a-1)(a+1))`
`=(a-1)^2/(a+1)`
`b)|a|=5`
`<=>` \(\left[ \begin{array}{l}a=5\\a=-5\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}Q=\dfrac{(5-1)^2}{5+1}=\dfrac83\\Q=\dfrac{(-5-1)^2}{-5+1}=-9\end{array} \right.\)
a) \(\left(x-2\right)\left(x^2-5x+1\right)-x\left(x^2+11\right)\)
\(=x\left(x^2-5x+1\right)-2\left(x^2-5x+1\right)-x\left(x^2+11\right)\)
\(=x^3-5x^2+x-2x^2+10x-2-x^3-11x\)
\(=-7x^2-2\)
b) \(\left(x-1\right)\left(x^2+x+1\right)+x^3-2\)
\(=x\left(x^2+x+1\right)-1\left(x^2+x+1\right)+x^3-2\)
\(=x^3+x^2+x-x^2-x-1+x^3-2\)
\(=2x^3-3\)
c) \(\left(x-y\right)\left(x+y\right)-2x\left(x-y\right)\)
\(=x\left(x+y\right)-y\left(x+y\right)-2x\left(x-y\right)\)
\(=x^2+xy-yx-y^2-2x^2+2xy\)
\(=-x^2-y^2+2xy\)
a, \(\left(x-2\right)\left(x^2-5x+1\right)-x\left(x^2+11\right)\)
\(=x^3-7x^2+11x-2-x^3-11x=-7x^2-2\)
b, \(\left(x-1\right)\left(x^2+x+1\right)+\left(x^3-2\right)\)
\(=x^3-1+x^3-2=2x^3-3\)
c, \(\left(x-y\right)\left(x+y\right)-2x\left(x-y\right)\)
\(=x^2-y^2-2x^2+2xy=-x^2-y^2+2xy\)