Question

Cho \(\frac{x-16}{9}=\frac{y-25}{16}=\frac{z+9}{25}\)  và 2x³-1=15

Tính x+y+z

Answer 1

Đặt \(\frac{x-16}{9}=\frac{y-25}{16}=\frac{x+9}{25}=k\)

\(\Rightarrow\hept{\begin{cases}x=9k+16\\y=16k+25\\z=25k-9\end{cases}}\Rightarrow x+y+z=9k+16+16k+25+25k-9=50k+32\)

Xét 2x³-1=15

=>2x³=15+1=16

=>x³=16:2=8

=>x³=2³

=>x=2

=>k=\(\frac{2-16}{9}=\frac{-14}{9}\)

=>x+y+z=\(50.\frac{-14}{9}+32=\frac{-412}{9}\)

Answer 2

Do 2x^3-1=15= =>2x^3=16 =>x^3m=8 =>x=2

ta co x-16/9 =y-25/16 =z+9/25 =x-16+y-25+z+25/   9+16+25  =x+y+z-32 /50  (1)

thay x=2 vao (1) ta co 2-16/9= -14/9=x+y+z-32 /50 =>x+y+z-32 =-700/9

=>x+y+z=-412/9