Question

Determinați x aparine lui R din proporțiile :
13 supra x = x supra 13
3x supra 2 = 2 supra 3x
Ajutați mă va rog

Answer 1

   
[tex]\displaystyle\\ \text{Ex. 1)}\\\\ \frac{13}{x}=\frac{x}{13}\\\\ \text{Egalam mezii cu extremii.}\\\\ x^2=13^2 ~~~\Big|~\sqrt{~~~} \\\\ \sqrt{x^2}=\sqrt{13^2}\\\\ x=\Big|13\Big|\\\\ x=\pm13\\\\ x_1=\boxed{13}\\\\ x_2=\boxed{-13}\\\\\\ \text{Ex. 2)}\\\\ \frac{3x}{2}=\frac{2}{3x}\\\\ \text{Egalam mezii cu extremii.}\\\\ 9x^2=2^2~~~\Big|~\sqrt{~~~}\\\\ \sqrt{9x^2}=\sqrt{2^2}\\\\ 3x=\Big|2\Big|\\\\ 3x=\pm2 x=\pm\frac{2}{3}\\\\ x_1=\boxed{\frac{2}{3}}\\\\ x_2=\boxed{-\frac{2}{3}} [/tex]

Answer 2

x²=13²
x²-13²=0
(x-13)(x+13)=0
x-13=0⇒x=13
x+13=0⇒x=-13


9x²=4
9x²-4=0
(3x)²-2²=0
(3x-2)(3x+2)=0
3x-2=0⇒3x=2⇒x=2/3
3x+2=0⇒3x=-2⇒x=-2/3