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1.
\(-3x^5y^4+3x^2y^3-7x^2y^3+5x^5y^4\)
\(=(-3x^5y^4+5x^5y^4)+(3x^2y^3-7x^2y^3)\)
\(=2x^5y^4-4x^2y^3\)
2.
\(\frac{1}{2}x^4y-\frac{3}{2}x^3y^4+\frac{5}{3}x^4y-x^3y^4\)
\(=(\frac{1}{2}x^4y+\frac{5}{3}x^4y)-(\frac{3}{2}x^3y^4+x^3y^4)\)
\(=\frac{13}{6}x^4y-\frac{5}{2}x^3y^4\)
3.
\(5x-7xy^2+3x-\frac{1}{2}xy^2\)
\(=(5x+3x)-(7xy^2+\frac{1}{2}xy^2)\)
\(=8x-\frac{15}{2}xy^2\)
4.
\(\frac{-1}{5}x^4y^3+\frac{3}{4}x^2y-\frac{1}{2}x^2y+x^4y^3\)
\(=(\frac{-1}{5}x^4y^3+x^4y^3)+(\frac{3}{4}x^2y-\frac{1}{2}x^2y)\)
\(=\frac{4}{5}x^4y^3+\frac{1}{4}x^2y\)
5.
\(\frac{7}{4}x^5y^7-\frac{3}{2}x^2y^6+\frac{1}{5}x^5y^7+\frac{2}{3}x^2y^6\)
\(=(\frac{7}{4}x^5y^7+\frac{1}{5}x^5y^7)+(-\frac{3}{2}x^2y^6+\frac{2}{3}x^2y^6)\)
\(=\frac{39}{20}x^5y^7-\frac{5}{6}x^2y^6\)
6.
\(\frac{1}{3}x^2y^5(-\frac{3}{5}x^3y)+x^5y^6=(\frac{1}{3}.\frac{-3}{5})(x^2.x^3)(y^5.y)+x^5y^6\)
\(=\frac{-1}{5}x^5y^6+x^5y^6=\frac{4}{5}x^5y^6\)
a,-200 x10 t10z3
b,\(\frac{-5}{4}\)x11 y5 z4
c,\(\frac{2}{15}\)x6 y6 z9
d,\(\frac{1}{7}\)x10 y6 z7
e,-4z6 y10 z6
1, \(\left(xy\right)^2-\frac{1}{2}x^2y^2+3xy^2.\left(-\frac{1}{3}x\right)\)
\(=x^2y^2-\frac{1}{2}x^2y^2-x^2y^2\)
\(=-\frac{1}{2}x^2y^2\)
2, \(4.\left(-\frac{1}{2}x\right)^2-\frac{3}{2}x.\left(-x\right)+\frac{1}{3}x^2\)
\(=x^2+\frac{3}{2}x^2+\frac{1}{3}x^2\)
\(=\frac{17}{6}x^2\)
3, \(-4.\left(2x\right)^2y^3+\frac{1}{2}xy.\left(-2xy^2\right)+\frac{1}{4}x^2y^3\)
\(=-16x^2y^3-x^2y^3+\frac{1}{4}x^2y^3\)
\(=-\frac{67}{4}x^2y^3\)
4, \(\frac{1}{3}x^4y-\frac{5}{3}x^3.\left(\frac{5}{2}xy\right)+\frac{3}{4}x^4y\)
\(=\frac{1}{3}x^4y-\frac{25}{6}x^4y+\frac{3}{5}x^4y\)
\(=-\frac{97}{30}x^4y\)
5, \(\left(-2x^3y^4\right)^2-5x^2y.\left(\frac{3}{4}x^4y^7\right)-\frac{2}{3}x^6y^8\)
\(=4x^6y^8-\frac{15}{4}x^6y^8-\frac{2}{3}x^6y^8\)
\(=-\frac{5}{12}x^6y^8\)
1.
\((\frac{1}{3}xy)^2.x^3+\frac{3}{2}(2x)^3(-\frac{7}{4}x^2y^2)-\frac{2}{3}x^5y^2\)
\(=(\frac{1}{9}x^2y^2)x^3+\frac{3}{2}(8x^3)(-\frac{7}{4}x^2y^2)-\frac{2}{3}x^5y^2\)
\(=\frac{1}{9}(x^2.x^3)y^2+(\frac{3}{2}.8.\frac{-7}{4})(x^3.x^2).y^2-\frac{2}{3}x^5y^2\)
\(=\frac{1}{9}x^5y^2-21x^5y^2-\frac{2}{3}x^5y^2=\frac{-194}{9}x^5y^2\)
2.
\(\frac{-2}{5}x^2y(-y^6)+\frac{3}{2}xy(\frac{-1}{15}xy^6)+(-2xy)^2y^5\)
\(=\frac{2}{5}x^2(y.y^6)+(\frac{3}{2}.\frac{-1}{15})(x.x).(y.y^6)+4x^2(y^2.y^5)\)
\(=\frac{2}{5}x^2y^7-\frac{1}{10}x^2y^7+4x^2y^7=\frac{43}{10}x^2y^7\)
3.
\(\frac{3}{7}xy^2z+\frac{1}{2}x^3y^2+\frac{1}{3}x^3y^2-\frac{3}{7}xy^2z\)
\(=(\frac{3}{7}xy^2z-\frac{3}{7}xy^2z)+(\frac{1}{2}x^3y^2+\frac{1}{3}x^3y^2)\)
\(=\frac{5}{6}x^3y^2\)
4.
\(\frac{2}{3}xy^2-\frac{5}{2}yz+\frac{1}{2}xy^2-\frac{2}{3}yz\)
\(=(\frac{2}{3}xy^2+\frac{1}{2}xy^2)-(\frac{5}{2}yz+\frac{2}{3}yz)\)
\(=\frac{7}{6}xy^2+\frac{19}{6}yz\)
5.
\(\frac{3}{2}xy^2z^5-\frac{5}{4}xyz^2+\frac{4}{3}xy^2z^5+\frac{1}{2}xyz^2\)
\(=(\frac{3}{2}xy^2z^5+\frac{4}{3}xy^2z^5)+(\frac{-5}{4}xyz^2+\frac{1}{2}xyz^2)\)
\(=\frac{17}{6}xy^2z^5-\frac{3}{4}xyz^2\)
Lời giải:
1.
\((-2x^4y^3z^7)^2(\frac{1}{4}xy^5)(-3x^2yz)^3(\frac{-1}{27}x^3yz^2)\)
\(=(4x^8y^6z^{14})(\frac{1}{4}xy^5)(-27x^6y^3z^3)(-\frac{1}{27}x^3yz^2)\)
\(=(4.\frac{1}{4}.-27.\frac{-1}{27})(x^8.x.x^6.x^3)(y^6.y^5.y^3.y)(z^{14}.z^3.z^2)\)
\(=x^{18}.y^{15}.z^{19}\)
2.
\(=(\frac{-1}{3}.\frac{4}{5}.\frac{-27}{10})(x.x^5.x^2)(y^2.y^6.y)(z.z.z^4)\)
\(=\frac{18}{25}.x^8.y^9.z^6\)
3.
\(=(49.x^{10}y^2z^4)(\frac{-1}{4}.x^3yz^7)(\frac{8}{21}x^5z^4)\)
\(=(49.\frac{-1}{4}.\frac{8}{21})(x^{10}.x^3.x^5)(y^2.y)(z^4.z^7.z^4)\)
\(=\frac{-14}{3}.x^{18}.y^3.z^{15}\)
4.
\(=(\frac{-1}{64}.x^8.y^9.z^{12})(4x^2y^2z^4)(\frac{-5}{3}x^4yz)\)
\(=(\frac{-1}{64}.4.\frac{-5}{3})(x^8.x^2.x^4)(y^9.y^2.y)(z^{12}.z^4.z)\)
\(=\frac{5}{48}.x^{14}.y^{12}.z^{17}\)
5.
\(=(\frac{1}{16}.x^8.y^4z^2)(-8xyz^2).(-\frac{1}{2}x^4yz)\)
\(=(\frac{1}{16}.-8.\frac{-1}{2})(x^8.x.x^4)(y^4.y.y)(z^2.z^2.z)\)
\(=\frac{1}{4}.x^{13}.y^6.z^5\)
a)x-3/x+5=5/7 suy ra 7.(x-3) = 5(x+5)
Tương đương : 7x - 21 = 5x + 25
7x - 5x = 25 + 21 = 46
2x = 46 suy ra : x = 46/2 = 23
Vậy x = 23
BÀi 2:
Cả 4 câu áp dụng tính chất này: \(\sqrt{a^2}=a\)
a)\(\sqrt{\frac{3^2}{7^2}}=\frac{3}{7}\)
b)\(\frac{\sqrt{3^2}+\sqrt{39^2}}{\sqrt{7^2}+\sqrt{92^2}}=\frac{3+39}{7+92}=\frac{42}{99}=\frac{14}{33}\)
c)\(\frac{\sqrt{3^2}-\sqrt{39^2}}{\sqrt{7^2}-\sqrt{91^2}}=\frac{3-39}{7-91}=\frac{-36}{-84}=\frac{3}{7}\)
d)\(\sqrt{\frac{39^2}{91^2}}=\frac{39}{91}=\frac{3}{7}\)
b)Vì BCNN(3;5) = 15
\(\Rightarrow\frac{x}{2}=\frac{y}{3}\Leftrightarrow\frac{x}{2.5}=\frac{y}{3.5}=\frac{x}{10}=\frac{y}{15};\frac{y}{5}=\frac{z}{7}\Leftrightarrow\frac{y}{5.3}=\frac{z}{7.3}=\frac{y}{15}=\frac{z}{21}\)
\(\Rightarrow\frac{x}{10}=\frac{y}{15}=\frac{z}{21}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(\frac{x}{10}=\frac{y}{15}=\frac{z}{21}=\frac{x+y+z}{10+15+21}=\frac{92}{46}=2\)
\(\Rightarrow\left\{{}\begin{matrix}x=2.10=20\\y=2.15=30\\z=2.21=42\end{matrix}\right.\)
Vậy...
c)Vì BCNN(2;3;5) = 30
\(\Rightarrow2x=3y=5z\Leftrightarrow\frac{2x}{30}=\frac{3y}{30}=\frac{5z}{30}=\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)
Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
WTFFFFFF>>>
d)dễ... áp dụng tính chất DTBN là ra 1/2 rồi tính
e)Áp dụng tính chất của dãy tỉ số bằng nhau, ta có:
\(x=\frac{y}{2}=\frac{z}{4}=\frac{4x}{4}=\frac{3y}{6}=\frac{2x}{8}=\frac{4x-3y+2x}{4-6+8}=\frac{36}{6}=6\)
\(\Rightarrow\left\{{}\begin{matrix}x=6.1=6\\y=6.2=12\\z=6.4=24\end{matrix}\right.\)
Vậy...
3/ ta để ý thấy ở số mũ sẽ có thừa số 1000-103=0
nên số mũ chắc chắn bằng 0
mà số nào mũ 0 cũng bằng 1 nên A=1
5/ vì |2/3x-1/6|> hoặc = 0
nên A nhỏ nhất khi |2/3x-6|=0
=>A=-1/3
6/ =>14x=10y=>x=10/14y
23x:2y=23x-y=256=28
=>3x-y=8
=>3.10/4y-y=8
=>6,5y=8
=>y=16/13
=>x=10/14y=10/14.16/13=80/91
8/106-57=56.26-56.5=56(26-5)=59.56
có chứa thừa số 59 nên chia hết 59
4/ tính x
sau đó thế vào tinh y,z
Bài 1:
a) \(\left(3x-\frac{4}{5}\right)^2+\left(2y+\frac{3}{7}\right)^2=0\)
\(\Rightarrow\left\{\begin{matrix}3x-\frac{4}{5}=0\\2y+\frac{3}{7}=0\end{matrix}\right.\rightarrow\left\{\begin{matrix}3x=\frac{4}{5}\\2y=-\frac{3}{7}\end{matrix}\right.\rightarrow\left\{\begin{matrix}x=\frac{4}{15}\\y=-\frac{3}{14}\end{matrix}\right.\)