ta có: \(x^{^2}\ge0\Leftrightarrow x^{^2}+2\ge2\)
\(\Leftrightarrow\) M=\(\dfrac{1}{x^{^2}+2}\le\dfrac{1}{2}\)
=> GTLN của M là \(\dfrac{1}{2}\) dấu "=" xảy ra khi \(\dfrac{1}{x^2+2}=\dfrac{1}{2}\Leftrightarrow x^2+2=2\Leftrightarrow x^2=0\)
\(\dfrac{2}{\left(x-1\right)\left(x-3\right)}+\dfrac{5}{\left(x-3\right)\left(x-8\right)}+\dfrac{12}{\left(x-8\right)\left(x-20\right)}+\dfrac{1}{x-20}=\dfrac{3}{4}\)
Tìm x
B = 1+ \(\dfrac{1}{2}\left(1+2\right)+\dfrac{1}{3}\left(1+2+3\right)+\dfrac{1}{4}\left(1+2+3+4\right)+.......+\dfrac{1}{x}\left(1+2+3+4+....+x\right)\)
Tìm số nguyên dương x để B = 115
ĐỀ 1:
1. Tính:
a. \(\dfrac{7}{23}\left[\left(\dfrac{-8}{6}\right)-\dfrac{45}{18}\right]\)
b. \(\dfrac{1}{5}:\dfrac{1}{10}-\dfrac{1}{3}\left(\dfrac{6}{5}-\dfrac{9}{4}\right)\)
c. \(\dfrac{3}{5}.\left(\dfrac{-8}{3}\right)-\dfrac{3}{5}:\left(-6\right)\)
d. \(\dfrac{1}{2}\left(\dfrac{4}{3}+\dfrac{2}{5}\right)-\dfrac{3}{4}\left(\dfrac{8}{9}+\dfrac{16}{3}\right)\)
e. \(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)
2. Tìm x, biết:
a. \(1\dfrac{2}{5}x+\dfrac{3}{7}=\dfrac{4}{5}\)
b. |x - 1,5| = 2
c. \(\dfrac{4}{5}-\left|x-\dfrac{1}{6}\right|=\dfrac{2}{3}\)
d. 3x . 2x = 216
e. \(\dfrac{1}{2}\left(x-\dfrac{1}{3}\right)+\dfrac{-1}{2}=\dfrac{3}{4}\)
* Lm nhanh nha
Ths you <3
Tìm nghiệm của các đa thức sau:
\(A=-\dfrac{2}{3}x-\dfrac{5}{9}\) \(B=x^2-\dfrac{4}{25}\) \(C=\dfrac{1}{2}x^3+\dfrac{4}{27}\) \(D=x^3-\dfrac{1}{8}x\)
\(E=-\dfrac{16}{81}+x^4\) \(F=-x.\left(-2x+3\right).\left(1-x^3\right)\) \(I=2.\left(2-x\right)+\dfrac{1}{2}\left(x-2\right)^2\) \(G=x^{100}-8.x^{97}\)
ĐỀ 2:
1. Tính:
A. \(\left(-\dfrac{2}{3}\right)^2+\left(-\dfrac{7}{8}\right)+\left(-\dfrac{11}{12}\right)\)
B. \(\left(\dfrac{-1}{3}\right)^2:\dfrac{1}{6}-2.\left(\dfrac{-1}{2}\right)^3\)\
C. \(\dfrac{-1}{5}-\left(\dfrac{1}{2}+\dfrac{3}{4}\right)^2:\dfrac{5}{8}\)
D. \(\left|\dfrac{-3}{2}+1,2\right|+1\dfrac{2}{3}:6\)
2. Tìm x, biết:
a. \(\dfrac{2}{3}x-\dfrac{1}{3}x=\dfrac{5}{12}\)
b. \(\left(x-\dfrac{12}{7}\right):1\dfrac{1}{5}=\dfrac{4}{7}\)
c. \(\dfrac{2}{5}+\left|x+1\right|=\dfrac{3}{4}\)
3. Tìm x, y biết:
a. \(\dfrac{x}{18}=\dfrac{y}{15}\)và x - y = -30
b. 7x = 9x và 10x - 8x = 68
c. \(\left(x-\dfrac{1}{2}\right)^{50}+\left(y+\dfrac{1}{3}\right)^{40}=0\)
* Lm nhanh nha
Tìm GTLN của đa thức sau:
\(R\left(x\right)=-x^2+\dfrac{2}{3}x+\dfrac{1}{5}\)
Tìm số nguyên x biết:
a. \(-4\dfrac{3}{5}.2\dfrac{4}{23}\)<x<\(-2\dfrac{3}{5}:1\dfrac{6}{15}\) b. \(-4\dfrac{1}{3}.\left(\dfrac{1}{2}-\dfrac{1}{6}\right)< x< -\dfrac{2}{3}\left(\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{3}{4}\right)\)
Tìm x, biết rằng:
a) \(\left(x-\dfrac{3}{4}\right)^2=0\)
b) \(\left(x-3\right)^2=1\)
c) \(\left(2x+1\right)^3=-8\)
d) \(\left(x-\dfrac{1}{4}\right)^2=\dfrac{1}{4}\)
1) Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{2010}=\dfrac{2010}{a}\)và a + b + c \(\ne\) \(-2010\). Tính a,b,c
2) Cho 3 tỉ số \(\dfrac{a}{b+c};\dfrac{b}{c+a};\dfrac{c}{a+b}\). Tính giá trị mỗi tỉ số.
3) Tìm GTNN của:
a) A = \(\sqrt{x+24}+\dfrac{4}{7}\)
b) B = \(\sqrt{2x+\dfrac{4}{13}}-\dfrac{13}{191}\)
4) Tìm GTLN của:
a) A = \(-\sqrt{x+\dfrac{5}{41}}+\dfrac{7}{12}\)
b) B = \(\dfrac{-5}{13}-\sqrt{x-\dfrac{2}{3}}\)
5) Tìm n, biết:
\(\sqrt{1+2+3+...+\left(n-1\right)+n+\left(n-1\right)+...+3+2+1=2010}\)
