3/a)\(M\left(x\right)=\frac{1}{2}x^2-3x-x^3+3\)
\(=-x^3+\frac{1}{2}x^2-3x+3\)
\(N\left(x\right)=-4x+x^2+\frac{1}{2}x^3+6\)
\(=\frac{1}{2}x^3+x^2-4x^3+6\)
b)Ta có:\(\text{A}\left(x\right)=M\left(x\right)-N\left(x\right)\)
hay \(\text{A}\left(x\right)=\left(-x^3+\frac{1}{2}x^2-3x+3\right)-\left(\frac{1}{2}x^3+x^2-4x+6\right)\)
\(=-x^3+\frac{1}{2}x^2-3x+3-\frac{1}{2}x^3-x^2+4x-6\)
\(=-\frac{3}{2}x^3-\frac{1}{2}x^2+x-3\)
Đặt\(\text{A}\left(x\right)=0\)
\(\Rightarrow-\frac{3}{2}x^3-\frac{1}{2}x^2+x-3=0\)
\(-\frac{3}{2}x^3-\frac{1}{2}x^2=-x+3\)
\(-2\left(x^3-x^2\right)=-x+3\)
\(x^3-x^2+x=3+2=5\)
\(x^2=5\)
\(\Rightarrow x=\sqrt{5}\)
Vậy \(\text{A}\left(x\right)\) có 1 nghiệm là \(\sqrt{5}\)
Bài 1: Thu gọn
a) \(\frac{1}{5}x^4y^3-3x^4y^3\)
b) \(5x^2y^5-\frac{1}{4}x^2y^5\)
c) \(\frac{1}{7}x^2y^3.\left(-\frac{14}{3}xy^2\right)-\frac{1}{2}xy.\left(x^2y^{\text{4}}\right)\)
d) \(\left(3xy\right)^2.\left(-\frac{1}{2}x^3y^2\right)\)
e) \(-\frac{1}{4}xy^2+\frac{2}{5}x^2y+\frac{1}{2}xy^2-x^2y\)
f) \(\frac{1}{2}x^4y.\left(-\frac{2}{3}x^3y^2\right)-\frac{1}{3}x^7y^3\)
g) \(\frac{1}{2}x^2y.\left(-10x^3yz^2\right).\frac{1}{4}x^5y^3z\)
h) \(4.\left(-\frac{1}{2}x\right)^2-\frac{3}{2}x.\left(-x\right)+\frac{1}{3}x^2\)
i) \(1\frac{2}{3}x^3y.\left(\frac{-1}{2}xy^2\right)^2-\frac{5}{4}.\frac{8}{15}x^3y.\left(-\frac{1}{2}xy^2\right)^2\)
k) \(-\frac{3}{2}xy^2.\left(\frac{3}{4}x^2y\right)^2-\frac{3}{5}xy.\left(-\frac{1}{3}x^4y^3\right)+\left(-x^2y\right)^2.\left(xy\right)^2\)
n) \(-2\frac{1}{5}xy.\left(-5x\right)^2+\frac{3}{4}y.\frac{2}{3}\left(-x^3\right)-\frac{1}{9}.\left(-x\right)^3.\frac{1}{3}y\)
m) \(\left(-\frac{1}{3}xy^2\right)^2.\left(3x^2y\right)^3.\left(-\frac{5}{2}xy^2z^3\right)^{^2}\)
p) \(-2y.\left|2\right|x^4y^5.\left|-\frac{3}{4}\right|x^3y^2z\)
Tìm x biết: \(\frac{4}{\left(x+2\right).\left(x+6\right)}+\frac{7}{\left(x+6\right).\left(x+13\right)}=\frac{2x+1}{\left(x+2\right).\left(x+16\right)}-\frac{3}{\left(x+13\right).\left(x+16\right)}\)
Tìm x biết: \(\frac{4}{\left(x+2\right).\left(x+6\right)}+\frac{7}{\left(x+6\right).\left(x+13\right)}=\frac{2x+1}{\left(x+2\right).\left(x+16\right)}-\frac{3}{\left(x+13\right).\left(x+16\right)}\)
Tìm x: \(\frac{3}{\left(x-4\right)\left(x-7\right)}+\frac{6}{\left(x-7\right)\left(x-13\right)}+\frac{15}{\left(x-13\right)\left(x-28\right)}+\frac{1}{x-28}=\frac{-1}{20}\)
Tìm \(x,\) biết:
a) \(4\left|3x-1\right|+\left|x\right|-2\left|x-5\right|+7\left|x-3\right|=12\)
b) \(3\left|x+4\right|-\left|2x+1\right|-5\left|x+3\right|+\left|x+9\right|=5\)
c) \( \left|2\frac{1}{5}-x\right|+\left|x-\frac{1}{5}\right|+8\frac{1}{5}=1,2\)
d) \(2\left|x+3\frac{1}{2}\right|+\left|x\right|-3\frac{1}{2}=\left|2\frac{1}{5}-x\right|\)
Tìm x, biết
a, 0,75-(x+\(\frac{1}{2}\))=\(\sqrt{\left(\frac{-4}{5}\right)^2}\)
b, \(\frac{\left(x-1\right)^2}{-3}\)=\(\frac{9}{x-1}\)(x khác 0)
Tìm GTLN
A=-200-|y-1|-|\(x^2\)-16|-\(\left(y+6\right)^{2010}\)-\(\sqrt{\left(x-4\right)^{2010}}\)
So Sánh:
a 7 + \(\sqrt{5}\) với \(\sqrt{48}+2\)
b \(\sqrt{\left(1-\sqrt{50}\right)^2}\) với 6
Tìm x,y biết: 3x2 - 3xy - 5x - y = -20
Tính:
3(x - 2) -4(2x + 1) - 5(2x + 3) = 50
\(\left(\frac{69}{167}-\left(2+\left(3+\left(4+5^{-1}\right)^{-1}\right)^{-1}\right)^{-1}\right)^{-1}\)
GIÚP MÌNH VỚI MAI NỘP RÒI!!!!!!!!
