Question

2x+5y/x+y = 4,5 afla : a) x/y=
b) 5x/2y=
c) x la puterea a 2+y la puterea a 2/y la puterea a 2

Answer 1

Observam ca
$4.5=\frac{9}{2}$
Atunci
$\frac{2x+5y}{x+y}=\frac{9}{2}\Rightarrow 2(2x+5y)=9(x+y)\Rightarrow 4x+10y=9x+9y\Rightarrow 10y-9y=9x-4x\Rightarrow y=5x \Rightarrow \frac{x}{y}=\frac{1}{5}$
b) $\frac{5}{2}*\frac{x}{y}=\frac{5}{2}*\frac{1}{5}=\frac{1}{2}$
c)[tex]\frac{x^{2}+y^{2}}{y^{2}}=\frac{x^{2}}{y^{2}}+1=(\frac{x}{y})^{2}+1=(\frac{1}{5})^{2}+1=\frac{1}{25}+1=\frac{1+25}{25}=\frac{26}{25}[/tex]

Answer 2

(2x+5y)/(x+y)=4,5   ⇔  2x+5y=4,5x+4,5y  adica: 5y-4,5y=4,5x-2x ⇒ 0,5y=2,5x
a).  din 0,5y=2,5x avem x/y = 0,5/2,5 = 1/5 ;

b).  5x/2y = 5/2*x/y=5/2*1/5=1/2 ;

c).  (x²+y²)/y² = x²/y² + y²/y² = (x/y)²+1 = 1/5² + 1 = 1/25+25/25=26/25 ;