a) `(x-1)/7 = 63/(x-1)`
`=> (x-1)(x-1) = 7.63`
`=>(x-1)^2 = 441`
`=>` \(\left[ \begin{array}{l}(x-1)^2=21^2\\(x-1)^2=(-21)^2\end{array} \right.\)
`=>`\(\left[ \begin{array}{l}x-1= 21\\x-1=-21\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=22\\x=-20\end{array} \right.\)
Vậy `x=22` hoặc `x=-20`
b)
Ta có: `x/2 = y/3 = z/4`
`=> (x/2)^2 = (y/3)^2 = (z/4)^2`
`=> x^2/4 = y^2/9 = z^2/16 = (3y^2)/(27) = (2z^2)/32`
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
`x^2/4 = (3y^2)/27 = (2z^2)/32= (x^2 + 3y^2 - 2z^2)/(4 + 27 - 32) = -16/-1 = 16`
+) `(x^2)/4=16=> x^2 =64`
`=>`\(\left[ \begin{array}{l}x=8\\x=-8\end{array} \right.\)
+) `(3y^2)/27 = 16 => 3y^2=432 =>y^2=144`
`=>` \(\left[ \begin{array}{l}x=12\\x=-12\end{array} \right.\)
+) `(2z^2)/32 = 16=> 2z^2=512 => z^2 =256`
`=>` \(\left[ \begin{array}{l}x=16\\x=-16\end{array} \right.\)
Vậy `x= 8; y= 12; z= 16` hoặc `x= -8; y= -12; z=-16`
