Question

$Daca \frac{x}{y} = 0,8 ,atunci \frac{x^{2} + y^{2} }{2 x^{2} - y^{2} } = ?$

Answer 1

0,8= 8/10 = 4/5

x/y=4/5

x=4y/5

(x²+y²)/ (2x²-y²)

(4y/5)²+y²  supra  2(4y/5)²-y²

(16y²/25 + y²)  supra (2 * 16y²/25 -y²  )

(16y²+25y²)/25  supra  (32y²/25 -y²)

41y²/25  supra (32y²-25y²)/25

41y²/25 supra 7y²/25=

=41y²/25 * 25/7y²=

=41/7

Answer 2

Simplificam fractia cu y² si obtinem:

$\dfrac{x^2+y^2}{2x^2-y^2}=\dfrac{(\frac xy)^2+1}{2(\frac xy)^2-1}=\dfrac{0,8^2+1}{2\cdot0,8^2-1}=\dfrac{1,64}{0,28}=\dfrac{164}{28}=\dfrac{41}{7}$