Question

Rezolvati in R ecuatia
3-x Supra x =3x+1 supra 7-x

Answer 1

(3-x)/x=(3x+1)/(7-x)
(3-x)(7-x)=x(3x+1)
21-3x-7x+x²=3x²+3x
x²-3x²-10x-3x+21=0
-2x²-13x+21=0   inmultim -1
2x²+13x-21=0
Δ=169+168=337
x1=(-13+√337)/4
x2=(-13-√337)/4

Answer 2

$\dfrac{3-x}{x}=\dfrac{3x+1}{7-x}$

$(3-x)(7-x)=x(3x+1)\Rightarrow 21-3x-7x+x^2=3x^2+x\Rightarrow$

$2x^2+11x-21=0$

$\Delta=289\Rightarrow \sqrt{\Delta}=17\Rightarrow x_1=\dfrac32;\ \ x_2=-7$