\(\dfrac{x}{3}=\dfrac{y}{4}\Leftrightarrow\dfrac{x^2}{9}=\dfrac{y^2}{16}\)

\(\dfrac{z}{5}=\dfrac{z^2}{25}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\dfrac{x^2+y^2}{9+16}=\dfrac{x^2+y^2}{25}=\dfrac{225}{25}=9\)

\(\Rightarrow x=\sqrt{9\cdot9}=9\)

\(\Rightarrow y=\sqrt{9\cdot16}=12\)

\(\Rightarrow z=\sqrt{9\cdot25}=15\)

\(\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\)

\(\Rightarrow\dfrac{x^2}{9}=\dfrac{y^2}{16}=\dfrac{x^2+y^2}{9+16}=\dfrac{225}{25}=9\)

\(\Rightarrow\left\{{}\begin{matrix}x^2=9.9=81\\y^2=16.9=144\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=9\\y=12\end{matrix}\right.\)

\(\Rightarrow z=\dfrac{9}{3}.5=15\)

Vậy \(\left\{{}\begin{matrix}x=9\\y=12\\z=15\end{matrix}\right.\) thỏa đề bài

x = 9

y = 12

z = 15

a: \(\left(x+5\right)^2-\left(x-5\right)^2-2x+1=0\)

=>\(x^2+10x+25-\left(x^2-10x+25\right)-2x+1=0\)

=>\(x^2+8x+26-x^2+10x-25=0\)

=>18x+1=0

=>\(x=-\dfrac{1}{18}\)

b: \(\left(2x-7\right)^2-\left(x+3\right)^2=3x^2+6\)

=>\(4x^2-28x+49-\left(x^2+6x+9\right)-3x^2-6=0\)

=>\(x^2-28x+43-x^2-6x-9=0\)

=>34-34x=0

=>34x=34

=>x=1

c: \(\left(3x+2\right)^2-9\left(x-5\right)\left(x+5\right)=225-5x\)

=>\(9x^2+12x+4-9\left(x^2-25\right)-225+5x=0\)

=>\(9x^2+17x+4-225-9x^2+225=0\)

=>17x+4=0

=>x=-4/17

Giải :

1 + 3 + 5 + .... + (2x-1) = [( 1 + 2x - 1 )x] : 2 = x².

Ta có : x² = 225 

           x² = 3² . 5² = (15)² ; => x=15

ta co 1+3+5+...+29=(1+29).15/2=225

nen 2x-1=19

2x=20

x=10

ket qua la:   x²=225  -> x=15

\(\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}:\frac{3}{5}+\frac{10}{9}\)

\(\Rightarrow\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{2}{7}.\frac{5}{3}+\frac{10}{9}\)

\(\Rightarrow\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{10}{21}+\frac{10}{9}\)

\(\Rightarrow\frac{2}{3}:\frac{x}{5}+\frac{5}{7}=\frac{100}{63}\)

\(\Rightarrow\frac{2}{3}:\frac{x}{5}=\frac{100}{63}-\frac{5}{7}\)

\(\Rightarrow\frac{2}{3}:\frac{x}{5}=\frac{55}{63}\)

\(\Rightarrow\frac{x}{5}=\frac{2}{3}:\frac{55}{63}\)

\(\Rightarrow\frac{x}{5}=\frac{2}{3}.\frac{63}{55}\)

\(\Rightarrow\frac{x}{5}=\frac{42}{55}\)

\(\Rightarrow x=\frac{42.5}{55}=\frac{42}{11}\)

Nên ta chọn đáp án D là đáp án đúng! 

( trong bài có dấu . tức là dấu dấu nhân bn nhé )

2/3 : x/5 + 5/7 = 2/7 : 3/5 + 10/9

2/3 : x/5 + 5/7 = 10/21 + 10/9

2/3 : x/5 + 5/7 = 100/63

2/3 : x/5 = 100/63 - 5/7

2/3 : x/5 = 55/63

2/3 . 5/x= 55/63

=) 5/x = 55/63 : 2/3

=) 5/x = 55/42

ta có : a/b = c/d =) a.d=b.c

(=) 55.x = 5.42

      55.x = 210

=)        x = 210 : 55 = 42/11

vậy đáp án đúng là D

 chúc bn học tốt

(x-1+1)(x+1):2=210

x(x+1):2=210

x(x+1)=420=20.21

=>x=20

a. 312; 318; 324; 330; 336.

b. 165; 180; 195; 210.