1) \(-452-\left(-67+75-452\right)\)

\(=-452+67-75+452\)

\(=-\left(452-67\right)-75+452\)

\(=-385-75+452\)

\(=-\left(385+75\right)+452\)

\(=-460+452\)

\(=-\left(460-452\right)\)

\(=-8\)

b) \(35-\left\{12-\left[-14+\left(-2\right)\right]\right\}\)

\(=35-\left[12-\left(-14-2\right)\right]\)

\(=35-\left\{12-\left[-\left(14+2\right)\right]\right\}\)

\(=35-\left[12-\left(-16\right)\right]\)

\(=35-\left(12+16\right)\)

\(=35-28\)

\(=7\)

c) \(-\left|-5\right|+\left(-19\right)+18+\left|11-4\right|-57\)

\(=-5-19+18+\left|7\right|-57\)

\(=-5-19+18+7-57\)

\(=-\left(5+19\right)+18+7-57\)

\(=-24+18+7-57\)

\(=-\left(24-18\right)+7-57\)

\(=-6+7-57\)

\(=-\left(6-7\right)-57\)

\(=-\left(-1\right)-57\)

\(=1-57\)

\(=-57+1\)

\(=-\left(57-1\right)\)

\(=-56\)

1) \(x^2y^2\left(y-x\right)+y^2z^2\left(z-y\right)-z^2x^2\left(z-x\right)\)

\(=x^2y^3-x^3y^2+y^2z^3-y^3z^2-z^2x^2\left(z-x\right)\)

\(=\left(y^2z^3-x^3y^2\right)-\left(y^3z^2-x^2y^3\right)-z^2x^2\left(z-x\right)\)

\(=y^2\left(z^3-x^3\right)-y^3\left(z^2-x^2\right)-z^2x^2\left(z-x\right)\)

\(=y^2\left(z-x\right)\left(z^2+zx+x^2\right)-y^3\left(z-x\right)\left(z+x\right)-z^2x^2\left(z-x\right)\)

\(=\left(z-x\right)\left[y^2\left(z^2+zx+x^2\right)-y^3\left(z+x\right)-z^2x^2\right]\)

\(=\left(z-x\right)\left[\left(y^2z^2+xy^2z+x^2y^2\right)-\left(y^3z+xy^3\right)-z^2x^2\right]\)

\(=\left(z-x\right)\left(y^2z^2+xy^2z+x^2y^2-y^3z-xy^3-z^2x^2\right)\)

\(=\left(z-x\right)\left[\left(y^2z^2-y^3z\right)-\left(x^2z^2-x^2y^2\right)+\left(xy^2z-xy^3\right)\right]\)

\(=\left(z-x\right)\left[y^2z\left(z-y\right)-x^2\left(z^2-y^2\right)+xy^2\left(z-y\right)\right]\)

\(=\left(z-x\right)\left[y^2z\left(z-y\right)-x^2\left(z-y\right)\left(z+y\right)+xy^2\left(z-y\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left[y^2z-x^2\left(z+y\right)+xy^2\right]\)

\(=\left(z-x\right)\left(z-y\right)\left(y^2z-x^2z-x^2y+xy^2\right)\)

\(=\left(z-x\right)\left(z-y\right)\left[\left(y^2z-x^2z\right)-\left(x^2y-xy^2\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left[z\left(y^2-x^2\right)-xy\left(x-y\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left[z\left(y-x\right)\left(y+x\right)+xy\left(y-x\right)\right]\)

\(=\left(z-x\right)\left(z-y\right)\left(y-x\right)\left[z\left(y+x\right)+xy\right]\)

\(=\left(z-x\right)\left(z-y\right)\left(y-x\right)\left(yz+xz+xy\right)\)

Ta có: \(2a=5b;7b=9c\)

\(2a=5b\Rightarrow\dfrac{a}{5}=\dfrac{b}{2}\Rightarrow\dfrac{a}{45}=\dfrac{b}{18}\)

\(7b=9c\Rightarrow\dfrac{b}{9}=\dfrac{c}{7}\Rightarrow\dfrac{b}{18}=\dfrac{c}{14}\)

\(\Rightarrow\dfrac{a}{45}=\dfrac{b}{18}=\dfrac{c}{14}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\dfrac{a}{45}=\dfrac{b}{18}=\dfrac{c}{14}=\dfrac{4a}{4.45}=\dfrac{5b}{5.18}=\dfrac{8c}{8.14}=\dfrac{4a-5b+8c}{180-90+112}=\dfrac{404}{202}=2\)

\(\dfrac{a}{45}=2\Rightarrow a=45.2=90\)

\(\dfrac{b}{18}=2\Rightarrow b=18.2=36\)

\(\dfrac{c}{14}=2\Rightarrow c=14.2=28\)

Vậy \(a=90\) và \(b=36\) và \(c=28\)

Là Bình

Tick cho mình

3) \(\dfrac{2}{2x+1}-\dfrac{1}{2x-1}-\dfrac{2}{1-4x^2}\)

\(=\dfrac{2}{2x+1}-\dfrac{1}{2x-1}+\dfrac{2}{4x^2-1}\)

\(=\dfrac{2}{2x+1}-\dfrac{1}{2x-1}+\dfrac{2}{\left(2x-1\right)\left(2x+1\right)}\) MTC: \(\left(2x-1\right)\left(2x+1\right)\)

\(=\dfrac{2\left(2x-1\right)}{\left(2x-1\right)\left(2x+1\right)}-\dfrac{2x+1}{\left(2x-1\right)\left(2x+1\right)}+\dfrac{2}{\left(2x-1\right)\left(2x+1\right)}\)

\(=\dfrac{2\left(2x-1\right)-\left(2x+1\right)+2}{\left(2x-1\right)\left(2x+1\right)}\)

\(=\dfrac{4x-2-2x-1+2}{\left(2x-1\right)\left(2x+1\right)}\)

\(=\dfrac{2x-1}{\left(2x-1\right)\left(2x+1\right)}\)

\(=\dfrac{1}{2x+1}\)

4) \(\dfrac{3x^2+5x+14}{x^3+1}+\dfrac{x-1}{x^2-x+1}-\dfrac{4}{x+1}\)

\(=\dfrac{3x^2+5x+14}{\left(x+1\right)\left(x^2-x+1\right)}+\dfrac{x-1}{x^2-x+1}-\dfrac{4}{x+1}\) MTC: \(\left(x+1\right)\left(x^2-x+1\right)\)

\(=\dfrac{3x^2+5x+14}{\left(x+1\right)\left(x^2-x+1\right)}+\dfrac{\left(x-1\right)\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}-\dfrac{4\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{\left(3x^2+5x+14\right)+\left(x-1\right)\left(x+1\right)-4\left(x^2-x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{3x^2+5x+14+x^2-1-4x^2+4x-4}{\left(x+1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{9x+9}{\left(x+1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{9\left(x+1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)

\(=\dfrac{9}{x^2-x+1}\)

Số các số chẵn nhỏ hơn 200 là: (998-2):2+1 = 499 (số)

2+4+6+...+996+998

=(2+996)+(4+994)...+998

=(998x499):2+998

=249999

a) \(4+5.\left(3+7\right):2-15\)

\(=4+5.10:2-15\)

\(=4+50:2-15\)

\(=4+25-15\)

\(=29-15\)

\(=14\)

Vậy chọn đáp án A

b) \(180-2.\left[7+3.\left(2.4-5\right)\right]\)

\(=180-2.\left[7+3.\left(8-5\right)\right]\)

\(=180-2.\left(7+3.3\right)\)

\(=180-2.\left(7+9\right)\)

\(=180-2.16\)

\(=180-32\)

\(=148\)

Vậy chọn đáp án B

Mất vệ sinh chứ gì!