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I . Trắc Nghiệm 1B . 2D . 3C . 5A II . Tự luận 2,a,Ta có: A+(x22y-2xy22+5xy+1)=-2x22y+xy22-xy-1 ⇔⇔ A=(-2x22y+xy22-xy-1) - (x22y-2xy22+5xy+1) =-2x22y+xy22-xy-1 - x22y+2xy22-5xy-1 =(-2x22y - x22y) + (xy22+ 2xy22) + (-xy - 5xy ) + (-1 - 1) = -3x22y + 3xy22 - 6xy - 2 b, thay x=1,y=2 vào đa thức A Ta có A= -3x22y + 3xy22 - 6xy - 2 = -3 . 122 . 2 + 3 .1 . 222 - 6 . 1 . 2 -2 = -6 + 12 - 12 - 2 = -8 3,Sắp xếp f(x) =9-x55+4x-2x33+x22-7x44 =9-x55-7x44-2x33+x22+4x g(x) = x55-9+2x22+7x44+2x33-3x =-9+x55+7x44+2x33+2x22-3x b,f(x) + g(x)=(9-x55-7x44-2x33+x22+4x) + (-9+x55+7x44+2x33+2x22-3x) =9-x55-7x44-2x33+x22+4x-9+x55+7x44+2x33+2x22-3x =(9-9)+(-x55+x55)+(-7x44+7x44)+(-2x33+2x33)+(x22+2x22)+(4x-3x) = 3x22 + x g(x)-f(x)=(-9+x55+7x44+2x33+2x22-3x) - (9-x55-7x44-2x33+x22+4x) =-9+x55+7x44+2x33+2x22-3x-9+x55+7x44+2x 33-x22-4x =(-9-9)+(x55+x55)+(7x44+7x44)+(2x33+2x33)+(2x22-x22)+(3x-4x) = -18 + 2x55 + 14x44 + 4x33 + x22 - x
I . Trắc Nghiệm
1B . 2D . 3C . 5A
II . Tự luận
2,a,Ta có: A+(x\(^2\)y-2xy\(^2\)+5xy+1)=-2x\(^2\)y+xy\(^2\)-xy-1
\(\Leftrightarrow\) A=(-2x\(^2\)y+xy\(^2\)-xy-1) - (x\(^2\)y-2xy\(^2\)+5xy+1)
=-2x\(^2\)y+xy\(^2\)-xy-1 - x\(^2\)y+2xy\(^2\)-5xy-1
=(-2x\(^2\)y - x\(^2\)y) + (xy\(^2\)+ 2xy\(^2\)) + (-xy - 5xy ) + (-1 - 1)
= -3x\(^2\)y + 3xy\(^2\) - 6xy - 2
b, thay x=1,y=2 vào đa thức A
Ta có A= -3x\(^2\)y + 3xy\(^2\) - 6xy - 2
= -3 . 1\(^2\) . 2 + 3 .1 . 2\(^2\) - 6 . 1 . 2 -2
= -6 + 12 - 12 - 2
= -8
3,Sắp xếp
f(x) =9-x\(^5\)+4x-2x\(^3\)+x\(^2\)-7x\(^4\)
=9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x
g(x) = x\(^5\)-9+2x\(^2\)+7x\(^4\)+2x\(^3\)-3x
=-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x
b,f(x) + g(x)=(9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x) + (-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x)
=9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x
=(9-9)+(-x\(^5\)+x\(^5\))+(-7x\(^4\)+7x\(^4\))+(-2x\(^3\)+2x\(^3\))+(x\(^2\)+2x\(^2\))+(4x-3x)
= 3x\(^2\) + x
g(x)-f(x)=(-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x) - (9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x)
=-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x-9+x\(^5\)+7x\(^4\)+2x \(^3\)-x\(^2\)-4x
=(-9-9)+(x\(^5\)+x\(^5\))+(7x\(^4\)+7x\(^4\))+(2x\(^3\)+2x\(^3\))+(2x\(^2\)-x\(^2\))+(3x-4x)
= -18 + 2x\(^5\) + 14x\(^4\) + 4x\(^3\) + x\(^2\) - x
a: \(=\dfrac{80}{9}x^3+\dfrac{1}{3}x^2-\dfrac{1}{3}x+18\)
Hệ số cao nhất là 80/9
Hệ số tự do là 18
Bậc là 3
b: \(f\left(3\right)=\dfrac{80}{9}\cdot27+\dfrac{1}{3}\cdot9-\dfrac{1}{3}\cdot3+18=260\)
\(f\left(-3\right)=\dfrac{80}{9}\cdot\left(-27\right)+\dfrac{1}{3}\cdot9+\dfrac{1}{3}\cdot3+18=-218\)
c: f(x)=-28 nên \(\dfrac{80}{9}x^3+\dfrac{1}{3}x^2-\dfrac{1}{3}x+46=0\)
\(\Leftrightarrow x\simeq-1.75\)
tìm nghiệm của đa thức sau:
a,\(\left(-\dfrac{5}{3}x^2+\dfrac{3}{5}\right)\left(x^2-2\right)\)
Xét \(\left(-\dfrac{5}{3}x^2+\dfrac{3}{5}\right)\left(x^2-2\right)\) \(=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-\dfrac{5}{3}x^2+\dfrac{3}{5}=0\\x^2-2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}-\dfrac{5}{3x}x^2=-\dfrac{3}{5}\\x^2=2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=\dfrac{9}{25}\\\left[{}\begin{matrix}x=-\sqrt{2}\\x=\sqrt{2}\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left[{}\begin{matrix}x=\dfrac{9}{25}\\x=-\dfrac{9}{25}\end{matrix}\right.\\\left[{}\begin{matrix}x=\sqrt{2}\\x=-\sqrt{2}\end{matrix}\right.\end{matrix}\right.\)
Vậy nghiệm của đa thức \(\left(-\dfrac{5}{3}x^2+\dfrac{3}{5}\right)\left(x^2-2\right)\) là \(\left\{\dfrac{9}{25};-\dfrac{9}{25};\sqrt{2};-\sqrt{2}\right\}\)
Bạn thay 0 vào rồi ra P(0) = 0 và Q(0) = -1/4
=> x = 0 là nghiệm của P(x) nhưng ko là nghiệm của Q(x)
1. Tìm n, biết:
a) \(\dfrac{-32}{\left(-2\right)^n}=4\)
\(\Rightarrow\dfrac{\left(-2\right)^5}{\left(-2\right)^n}=\left(-2\right)^2\)
\(\Rightarrow\left(-2\right)^n.\left(-2\right)^2=\left(-2\right)^5\)
(-2)n + 2 = (-2)5
n + 2 = 5
n = 5 - 2
n = 3.
b) \(\dfrac{8}{2^n}=2\)
\(\Rightarrow\dfrac{2^3}{2^n}=2\)
\(\Rightarrow\) 2n . 2 = 23
n + 1 = 3
n = 3 - 1
n = 2.
c) \(\left(\dfrac{1}{2}\right)^{2n-1}=\dfrac{1}{8}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{2n-1}=\left(\dfrac{1}{2}\right)^3\)
2n - 1 = 3
2n = 3 + 1
2n = 4
n = 4 : 2
n = 2.
2. Tính:
a) \(\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{4}\right)^2\)
\(=\left(\dfrac{1}{2}\right)^3.\left[\left(\dfrac{1}{2}\right)^2\right]^2\)
\(=\left(\dfrac{1}{2}\right)^3.\left(\dfrac{1}{2}\right)^4\)
\(=\left(\dfrac{1}{2}\right)^7\)
\(=\dfrac{1}{128}\)
b) 273 : 93
= (33)3 : (32)3
= 39 : 36
= 33
= 27
c) 1252 : 253
= (53)2 : (52)3
= 56 : 56
= 1
d) \(\dfrac{27^2.8^5}{6^6.32^3}\)
\(=\dfrac{\left(3^3\right)^2.\left(2^3\right)^5}{6^6.\left(2^5\right)^3}\)
\(=\dfrac{3^6.2^{15}}{6^6.2^{15}}\)
\(=\dfrac{3^6}{6^6}\)
\(=\dfrac{1}{64}.\)
B2 :
b) 27\(^3\): 9\(^3\)= (27:9)\(^3\)= 3\(^3\)
c) 125\(^2\): 25\(^3\)= 15625 : 15625 = 1
3B
2: Ko có câu nào đúng