\(\frac{x^2+15}{x^2+3}\)
\(=\frac{x^2+3+12}{x^2+3}\)
\(=\frac{x^2+3}{x^2+3}+\frac{12}{x^2+3}\)
\(=1+\frac{12}{x^2+3}\)
\(x^2\ge0\)
\(x^2+3\ge3\)
\(\frac{12}{x^2+3}\le4\)
\(1+\frac{12}{x^2+3}\le5\)
ĐS: 5
the maximum value of C=x2+8/(2(x2+2)
Find the maximum value of:
a) \(-3x^2-9x-25\)
b) \(x-x^2\)
c) \(-x^2+7x+12\)
the maximum of A=6/2(x-3)2+3
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) \(-2y.\left|2\right|x^4y^5.\left|-\frac{3}{4}\right|x^3y^2z\)
Tính
A) \(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-1\frac{15}{17}+\frac{2}{3}\)
B) \(\left(-2\right)^3\times\left(\frac{3}{4}-0,25\right):\left(2\frac{1}{4}-1\frac{1}{6}\right)\)
Tìm x
A) \(4\frac{1}{3}:\frac{\chi}{4}=6:0,3\)
B) \(\left(2^3:4\right)\times2^{\left(\chi+1\right)}=64\)
a, \(\frac{-5}{8}-x:3\frac{5}{6}+7\frac{3}{4}=-2\)
b,\(\frac{3}{4}:2\frac{4}{9}-\left|-3x+2\frac{2}{3}\right|=\frac{3}{4}\)
c, \(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{625}\)
d,\(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
1.tìm x
a.\(\left(3^1_4:x\right).\left(-1^1_4\right)=\frac{-5}{3}-\frac{5}{6}\)
b.\(\frac{-1}{4}-\frac{3}{4}:x=\frac{-11}{36}\)
c.\(\left(-1^1_5+x\right):\left(-3^3_5\right)=\frac{-7}{4}+\frac{1}{4}:\frac{1}{8}\)
d.\(\frac{-22}{15}x+\frac{1}{3}=\left|-\frac{2}{3}+\frac{1}{5}\right|\)
Bài 1: Thực hiện phép tính
a) \(2\frac{1}{2}-\frac{4}{3}+\left(\frac{-1}{3}\right)^4\)
b) \(\frac{1}{7}-\left(-\frac{3}{14}\right)+\frac{1}{2}\)
c) -12:\(\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
d) \(\left(2^2:\frac{4}{3}-\frac{1}{2}\right).\frac{6}{5}-17\)
Bài 2:Tìm x biết
a) \(\frac{4}{7}-x=\frac{1}{3}\)
b) \(x-\frac{2}{3}=-\frac{6}{7}\)
c) \(\left|x-5\right|=7\)
d) \(\frac{2}{3}-1\frac{4}{15}x=\frac{-3}{5}\)
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) \(2\left|x+3\frac{1}{2}\right|+\left|x\right|-3\frac{1}{2}=\left|2\frac{1}{5}-x\right|\)
