Các bạn giúp mình giải với nhé! Đúng thì mình k đúng nhé. Cảm ơn các bạn nhiều lắm. Yêu cả nhà.

\(1.\left(x-5\right)^{23}.\left(y+2\right)^7=0\)

\(\Rightarrow\hept{\begin{cases}\left(x-5\right)^{23}=0\\\left(y+2\right)^7=0\end{cases}\Rightarrow\hept{\begin{cases}\left(x-5\right)^{23}=0^{23}\\\left(y+2\right)^7=0^7\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}x-5=0\\y+2=0\end{cases}\Rightarrow\hept{\begin{cases}x=0+5\\y=0-2\end{cases}}}\)\(\Rightarrow\hept{\begin{cases}x=5\\y=-2\end{cases}}\)

Vậy \(\left(x;y\right)=\left(5;-2\right)\)

2. \(A=\left(x-2\right)^2+|y+3|+7\)

Ta có :

\(\hept{\begin{cases}\left(x-2\right)^2\ge0\forall x\\|y+3|\ge0\forall y\end{cases}}\)

\(\Rightarrow\left(x-2\right)^2+|y+3|\ge0\forall x;y\)

\(\Rightarrow\left(x-2\right)^2+|y+3|+7\ge7\forall x;y\)

\(\Rightarrow A\ge7\forall x;y\)

Dấu bằng xảy ra

\(\Leftrightarrow\hept{\begin{cases}\left(x-2\right)^2=0\\|y+3|=0\end{cases}\Leftrightarrow\hept{\begin{cases}x-2=0\\y+3=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=2\\y=-3\end{cases}}}\)

Vậy GTNN của A là 7 khi \(\left(x;y\right)=\left(2;-3\right)\)

=>7^x*49+7^x*2=51

=>7^x*51=51

=>7^x=1

=>x=0

\(7^{x+2}+7^x\cdot2=51\\ \Leftrightarrow7^x\cdot7^2+7^x\cdot2=51\\ \Leftrightarrow7^x\cdot51=51\\ \Leftrightarrow7^x=1\\ \Leftrightarrow x=0\)

Bài 1:

a) \(=\dfrac{8}{15}\left(\dfrac{7}{13}+\dfrac{6}{13}\right)=\dfrac{8}{15}.1=\dfrac{8}{15}\)

b) \(=\dfrac{3.3-7-2.4}{12}=-\dfrac{6}{12}=-\dfrac{1}{2}\)

Bài 2:

 \(\dfrac{x}{2,7}=-\dfrac{2}{3,6}\Rightarrow x=\dfrac{\left(-2\right).2,7}{3,6}\Rightarrow x=-\dfrac{3}{2}\)

Bài 3:

\(\dfrac{x}{2}=\dfrac{y}{5}=\dfrac{x+y}{2+5}=-\dfrac{21}{7}=-3\)

\(\Rightarrow\left\{{}\begin{matrix}x=\left(-3\right).2=-6\\y=\left(-3\right).5=-10\end{matrix}\right.\)

5 ( x - 1 ) - 7 ( x - 2 ) = 2x - 39

<=> 5x - 5 - 7x + 14 = 2x - 39

<=> 5x - 7x - 2x = -39 + 5 - 14

<=> -4x = -48

<=> x = 12

x - 3 - 14.( x-2 )= -3x -3\(\Rightarrow\chi-3-28-14\chi-28=-3\chi-3\)

\(\Rightarrow\chi-3-28+3=-3\chi-3\)

\(\Rightarrow\chi-28=11\chi\)

\(\Rightarrow\chi-11\chi=28\)

\(\Rightarrow10\chi=28\Rightarrow\chi=2,8\left(kot.m\chi\inℤ\right)\) 

HTDT-sai-rùi

x-3-14(x-2)=-3x-3

x-3+28-14x=-3x-3

-13x+35=-3x-3

-13x+3x=-3-35

-10x=-38

x=38/10=19/5

Lời giải:

$49x=|2x+7|+|2x+7^2|+....+|2x+7^{50}|\geq 0$

$\Rightarrow x\geq 0$

$\Rightarrow 2x+7>0; 2x+7^2>0;....; 2x+7^{50}>0$

Do đó bài toán trở thành:

$(2x+7)+(2x+7^2)+....+(2x+7^{50})=49x$

$\underbrace{(2x+2x+...+2x)}_{50}+(7+7^2+....+7^{50})=49x$

$\Rightarrow 100x+(7+7^2+....+7^{50})=49x$

$\Rightarrow 7+7^2+....+7^{50} = -51x>0$

$\Rightarrow x<0$ (vô lý - loại) 

Vậy không tồn tại $x$ thỏa mãn đề.

Bài 1:

a) \(\dfrac{9}{20}-\dfrac{8}{15}\times\dfrac{5}{12}\)

\(=\dfrac{9}{20}-\dfrac{2}{9}\)

\(=\dfrac{41}{180}\)

b) \(\dfrac{2}{3}\div\dfrac{4}{5}\div\dfrac{7}{12}\)

\(=\dfrac{2}{3}\times\dfrac{5}{4}\times\dfrac{12}{7}\)

\(=\dfrac{5}{6}\times\dfrac{12}{7}\)

\(=\dfrac{10}{7}\)

c) \(\dfrac{7}{9}\times\dfrac{1}{3}+\dfrac{7}{9}\times\dfrac{2}{3}\)

\(=\dfrac{7}{9}\times\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\)

\(=\dfrac{7}{9}\times1\)

\(=\dfrac{7}{9}\)

Bài 2:

a) \(2\times\left(x-1\right)=4026\)

\(\left(x-1\right)=4026\div2\)

\(x-1=2013\)

\(x=2014\)

Vậy: \(x=2014\)

b) \(x\times3,7+6,3\times x=320\)

\(x\times\left(3,7+6,3\right)=320\)

\(x\times10=320\)

\(x=320\div10\)

\(x=32\)

Vậy: \(x=32\)

c) \(0,25\times3< 3< 1,02\)

\(\Leftrightarrow0,75< 3< 1,02\) ( S )

=> \(0,75< 1,02< 3\)

\(7^x-7^{x+2}=-2352=7^x-7^x.7^2\Rightarrow7^x-7^x.49=-2352\Rightarrow7^x.-48=-2352\)

\(\Rightarrow7^x=-2352:-48=49=7^2\Rightarrow x=2\)

\(7^x-7^{x+2}=-2352\)

\(7^x\left(1-49\right)=-2352\)

\(7^x.\left(-48\right)=-2352\)

\(\Rightarrow7^x=49\Leftrightarrow x=2\)

\(7^x-7^{x+2}=-2352\)

\(\Rightarrow7^x-7^x.7^2=-2352\)

\(\Rightarrow7^x.\left(1-49\right)=-2352\)

\(\Rightarrow7^x.\left(-48\right)=-2352\)

\(\Rightarrow7^x=49=7^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

a) Ta có:

1; 4; 7;...; 100 có (100 - 1) : 3 + 1 = 34 (số)

1 + 4 + 7+ ... + 100 = (100 + 1) × 34 : 2

= 101 × 17

(1 + 4 + 7 + ... + 100) : a = 17

101 × 17 : a = 17

a = 101 × 17 : 17

a = 100

b) (X - 1/2) × 5/3 = 7/4 - 1/2

(X - 1/2) × 5/3 = 5/4

X - 1/2 = 5/4 : 5/3

X - 1/2 = 3/4

X = 3/4 + 1/2

X = 5/4

a) (1 + 4 + 7 +...+ 100) : a = 17

1717 : a = 17

a = 101

b) \(\left(x-\dfrac{1}{2}\right)\times\dfrac{5}{3}=\dfrac{7}{4}-\dfrac{1}{2}\)

\(\left(x-\dfrac{1}{2}\right)\times\dfrac{5}{3}=\dfrac{10}{8}\)

\(\left(x-\dfrac{1}{2}\right)=\dfrac{10}{8}\div\dfrac{5}{3}\)

\(\left(x-\dfrac{1}{2}\right)=\dfrac{10}{8}\times\dfrac{3}{5}\)

\(\left(x-\dfrac{1}{2}\right)=\dfrac{3}{4}\)

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

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

\(x=\dfrac{5}{4}\)

a. (1+4+7+...+100):a=17 

=> ( 100 + 1) x 32 : 2 : a = 17

=> 1717 : a = 17 

=> a = 101

b. \(\left(X-\dfrac{1}{2}\right).\dfrac{5}{3}=\dfrac{7}{4}-\dfrac{2}{4}\)

\(\left(X-\dfrac{1}{2}\right).\dfrac{5}{3}=\dfrac{5}{4}\)

\(X-\dfrac{1}{2}=\dfrac{3}{4}\)

\(X=\dfrac{1}{4}\)