\(\sqrt{25}.\left(0,4-1\dfrac{1}{2}\right):\left[\left(-2\right)^3:\dfrac{8}{11}\right]\)

\(=5.\left(\dfrac{2}{5}-\dfrac{3}{2}\right):\left(-8:\dfrac{8}{11}\right)\)

\(=5.\left(-\dfrac{11}{10}\right):\left(-11\right)\)

\(=\dfrac{-11}{2}:\left(-11\right)\)

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

Gọi a là chiều dài, b là chiều rộng của hình chữ nhật

Diện tích ban đầu: ab

Diện tích lúc sau: \(6a.\dfrac{b}{2}=3ab\)

Vậy diện tích tăng 3 lần

Chọn B

\(\Delta ABC\) vuông tại A

\(\Rightarrow BC^2=AB^2+AC^2\left(Pytago\right)\)

\(=3^2+4^2\)

\(=25\)

\(\Rightarrow BC=5\left(cm\right)\)

Đường trung tuyến AM là đường trung tuyến ứng với cạnh huyền BC

\(\Rightarrow AM=\dfrac{BC}{2}=\dfrac{5}{2}=2,5\left(cm\right)\)

Chọn C

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

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

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

Chọn B và C

ĐKXĐ:

\(2x-6\ne0\)

\(\Leftrightarrow2x\ne6\)

\(\Leftrightarrow x\ne\dfrac{6}{2}\)

\(\Leftrightarrow x\ne3\)

Chọn A

\(ƯCLN\left(1;2;3;...;100\right)+ƯCLN\left(1^2;2^2;3^2;...;100^2\right)+ƯCLN\left(1^3;2^3;3^3;...;100^2\right)+...+ƯCLN\left(1^{100};2^{100};3^{100};...;100^{100}\right)\)

\(=1+1+1+...+1\) (100 chữ số 1)

\(=100\)

Bài 10

a) \(5-2x=13\)

\(2x=5-13\)

\(2x=-8\)

\(x=-\dfrac{8}{2}\)

\(x=-4\)

b) \(-45:\left(3x-17\right)=\left(-3\right)^2\)

\(-45:\left(3x-17\right)=9\)

\(3x-17=-45:9\)

\(3x-17=-5\)

\(3x=-5+17\)

\(3x=12\)

\(x=\dfrac{12}{3}\)

\(x=4\)

c) \(-12x-23=\left(-3\right)^3+\left(-7\right).8\)

\(-12x-23=-27-56\)

\(-12x-23=-83\)

\(-12x=-83+23\)

\(-12x=-60\)

\(x=\dfrac{-60}{-12}\)

\(x=5\)

d) \(x^2-16=3^8:3^6\)

\(x^2-16=9\)

\(x^2=9+16\)

\(x^2=25\)

\(x=5;x=-5\)

e) \(x^3+15=-12\)

\(x^3=-12-15\)

\(x^3=-27\)

\(x^3=\left(-3\right)^3\)

\(x=-3\)

f) \(3x^2-7=5\)

\(3x^2=5+7\)

\(3x^2=12\)

\(x^2=\dfrac{12}{3}\)

\(x^2=4\)

\(x=2;x=-2\)

g) \(\left(x-5\right)\left(x^2-9\right)=0\)

\(x-5=0;x^2-9=0\)

*) \(x-5=0\)

\(x=5\)

*) \(x^2-9=0\)

\(x^2=9\)

\(x=-3;x=3\)

Vậy \(x=-3;x=3;x=5\)

Bài 9

a) \(\left(x-2\right)\left(y+3\right)=5\)

\(\Rightarrow\left(x-2;y+3\right)\in\left\{\left(1;5\right);\left(-1;-5\right);\left(5;1\right);\left(-5;-1\right)\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(3;2\right);\left(1;-8\right);\left(7;-2\right);\left(-3;-4\right)\right\}\)

b) \(\left(x+4\right)\left(y-5\right)=3\)

\(\Rightarrow\left(x+4;y-5\right)\in\left\{\left(1;3\right)\left(-1;-3\right);\left(3;1\right);\left(-3;-1\right)\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(-3;8\right);\left(-5;2\right);\left(-1;6\right);\left(-7;4\right)\right\}\)

c) \(\left(2x+1\right)\left(y-3\right)=8\)

\(\Rightarrow\left(2x+1;y-3\right)\in\left\{\left(-8;-1\right);\left(-4;-2\right);\left(-2;-4\right);\left(-1;-8\right);\left(1;8\right);\left(2;4\right)\left(4;2\right);\left(8;1\right)\right\}\)

\(\Rightarrow\left(2x;y\right)\in\left\{\left(-9;2\right);\left(-5;1\right);\left(-3;-1\right);\left(-2;-5\right);\left(0;11\right);\left(1;7\right);\left(3;5\right);\left(7;4\right)\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(-\dfrac{9}{2};2\right);\left(-\dfrac{5}{2};1\right);\left(-\dfrac{3}{2};-1\right);\left(-1;-5\right);\left(0;11\right);\left(\dfrac{1}{2};7\right);\left(\dfrac{3}{2};5\right);\left(\dfrac{7}{2};4\right)\right\}\)

Mà \(x;y\in Z\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(-1;-5\right);\left(0;11\right)\right\}\)

d) \(\left(3x-2\right)\left(2y-3\right)=12\)

\(\Rightarrow\left(3x-2;2y-3\right)\in\left\{\left(-12;-1\right);\left(-6;-2\right);\left(-4;-3\right);\left(-3;-4\right);\left(-2;-6\right);\left(-1;-12\right);\left(1;12\right);\left(2;6\right);\left(3;4\right);\left(4;3\right);\left(6;2\right);\left(12;1\right)\right\}\)

\(\Rightarrow\left(3x;2y\right)\in\left\{\left(-10;2\right);\left(-4;1\right);\left(-2;0\right);\left(-1;-1\right);\left(0;-3\right);\left(1;-9\right);\left(3;15\right);\left(4;9\right);\left(5;7\right);\left(6;6\right);\left(8;5\right);\left(14;4\right)\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(-\dfrac{10}{3};1\right);\left(-\dfrac{4}{3};\dfrac{1}{2}\right);\left(-\dfrac{2}{3};0\right);\left(-\dfrac{1}{3};-\dfrac{1}{2}\right);\left(0;-\dfrac{3}{2}\right);\left(\dfrac{1}{3};-\dfrac{9}{2}\right);\left(1;\dfrac{15}{2}\right);\left(\dfrac{4}{3};\dfrac{9}{2}\right);\left(\dfrac{5}{3};\dfrac{7}{2}\right);\left(2;3\right):\left(\dfrac{8}{3};\dfrac{5}{2}\right);\left(\dfrac{14}{3};2\right)\right\}\)

Mà \(x,y\in Z\)

\(\Rightarrow\left(x;y\right)=\left(2;3\right)\)

e) \(\left(x+7\right)\left(2x-y\right)=3\)

\(\Rightarrow\left(x+7;2x-y\right)\in\left\{\left(-3;-1\right);\left(-1;-3\right);\left(1;3\right);\left(3;1\right)\right\}\)

\(\Rightarrow\left(x;2x-y\right)\in\left\{\left(-10;-1\right);\left(-8;-3\right);\left(-6;3\right);\left(-4;1\right)\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(-10;-19\right);\left(-8;-13\right);\left(-6;-15\right);\left(-4;-9\right)\right\}\)

f) \(\left(2x-1\right)\left(y^2-13\right)=4\)

\(\Rightarrow\left(2x-1;y^2-13\right)\in\left\{\left(-4;-1\right);\left(-2;-2\right);\left(-1;-4\right);\left(1;4\right);\left(2;2\right)\left(4;1\right)\right\}\)

\(\Rightarrow\left(2x;y^2\right)\in\left\{\left(-3;12\right);\left(-1;11\right);\left(0;7\right);\left(2;17\right);\left(3;15\right);\left(5;14\right)\right\}\)

Do \(y\in Z\Rightarrow y^2\) là số chính phương

Mà \(12;11;7;17;15;14\) không phải số chính phương

\(\Rightarrow\) Không tìm được cặp giá trị \(\left(x;y\right)\in Z\) thỏa mãn yêu cầu đề bài

10 lần tổng 2 số bằng:

10 x 10,74 = 107,4

Số thứ nhất bằng:

113,38 - 107,4= 5,98

10 lần Số thứ hai bằng:

107,4 - (5,98 x 10)= 47,6

Số thứ hai gấp lên 100 lần bằng:

47,6 x (100:10) = 476

Đ.số: 100 lần số thứ hai là 476

-55

143 nhe 

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