Question

determinati valoarea reala pozitiva a lui x știind ca:
a) x/5=5/x
b) 10/x=x/3,6
c)x/0,75=0,(3)/x
d)0,5/x=x/2

​

Answer 1

Răspuns:

a)

$\frac{x}{5} = \frac{5}{x} \\ x \times x = 5 \times 5 \\ x {}^{2} = 25 \\ x = \sqrt{25} \\ x = 5$

b)

$\frac{10}{x} = \frac{x}{3.6} \\ x \times x = 10 \times 3.6 \\ x {}^{2} = 36 \\ x = \sqrt{36} \\ x = 6$

d)

$\frac{0.5}{x} = \frac{x}{2} \\ x \times x = 0.5 \times 2 \\ x {}^{2} = 1 \\ x = \sqrt{1} \\ x = 1$

c)

$\frac{x}{0.75} = \frac{0.(3)}{x} \\ x \times x = 0.75 \times 0.(3) \\ x {}^{2} = 0.75 \times \frac{3}{9} \\ x {}^{2} = 0.75 \times \frac{1}{3} \\ x {}^{2} = \frac{0.75}{3} \\ x {}^{2} = 0.25 \\ x = \sqrt{0.25} \\ x = 0.5$

CE TREBUIE SA STIM PENTRU A PUTEA REZOLVA :

$\huge \frac{a}{b} = \frac{c}{d} \\ \\ \huge{b \times c = a \times d}$