Cho 2 đơn thức:
A = 5/7(x6y3) ; B = -14/15x4y
Chứng minh 2 đơn thức A và B không thể cùng có giá trị dương.
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a)\(\dfrac{3\left(x-y\right)^4+2\left(x-y\right)^3-5\left(x-y\right)^2}{\left(y-x\right)^2}=\dfrac{\left(x-y\right)^2\left[3\left(x-y\right)^2+2\left(x-y\right)-5\right]}{\left(x-y\right)^2}=3x^2-6xy+3y^2+2x-2y-5\)
b) \(\dfrac{\left(x-2y\right)^3}{x^2-4xy+4y^2}=\dfrac{\left(x-2y\right)^3}{\left(x-2y\right)^2}=x-2y\)
c) \(\dfrac{x^3+y^3}{x+y}=\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{x+y}=x^2-xy+y^2\)
a: \(\dfrac{3\left(x-y\right)^4+2\left(x-y\right)^3-5\left(x-y\right)^2}{\left(y-x\right)^2}\)
\(=\dfrac{3\left(x-y\right)^4+2\left(x-y\right)^3-5\left(x-y\right)^2}{\left(x-y\right)^2}\)
\(=3\left(x-y\right)^2+2\left(x-y\right)-5\)
b: \(\dfrac{\left(x-2y\right)^3}{x^2-4xy+4y^2}\)
\(=\dfrac{\left(x-2y\right)^3}{\left(x-2y\right)^2}\)
=x-2y
c: \(\dfrac{x^3+y^3}{x+y}\)
\(=\dfrac{\left(x+y\right)\left(x^2-xy+y^2\right)}{x+y}\)
\(=x^2-xy+y^2\)
a) \(\dfrac{9}{5}+\dfrac{9}{5}:\dfrac{9}{5}\)
\(=\dfrac{9}{5}+\dfrac{9}{5}\times\dfrac{5}{9}\)
\(=\dfrac{9}{5}+1\)
\(=\dfrac{14}{5}\)
b) \(\dfrac{7}{5}-\dfrac{1}{2}\times\dfrac{1}{3}\)
\(=\dfrac{7}{5}-\dfrac{1}{6}\)
\(=\dfrac{42}{30}-\dfrac{5}{30}\)
\(=\dfrac{37}{30}\)
\(a,\dfrac{9}{5}+\dfrac{9}{5}:\dfrac{9}{5}\)
\(=\dfrac{9}{5}+\dfrac{9}{5}\times\dfrac{5}{9}\)
\(=\dfrac{9}{5}+1\)
\(=\dfrac{9}{5}+\dfrac{5}{5}\)
\(=\dfrac{14}{5}\)
\(b,\dfrac{7}{5}-\dfrac{1}{2}\times\dfrac{1}{3}\)
\(=\dfrac{7}{5}-\dfrac{1}{6}\)
\(=\dfrac{42}{30}-\dfrac{5}{30}\)
\(=\dfrac{37}{30}\)
\(A=\dfrac{7}{3}+\dfrac{5}{7}+\dfrac{2}{3}-\dfrac{7}{12}+\dfrac{5}{2}=3+\dfrac{221}{84}=\dfrac{473}{84}\)
=(1-2-3+4)+(5-6-7+8)+...+(2017-2018-2019+2020)+2021-2022-2023
=0+0+...+0-1-2023
=-2024
\(A=-\frac{3}{8}x^2y.\frac{2}{3}xy^2.z^2.\frac{4}{5}x^3y\)
\(=\left(-\frac{3}{8}.\frac{2}{3}.\frac{4}{5}\right)\left(x^2xx^3\right)\left(yy^2y\right)z^2\)
\(=-\frac{1}{5}x^6y^4z^2\)