Question

Știind că x/y=3/4 calculați:
a)x²+y²/x²
b)2x+5y/5x-y
c)7x-2y/x+y​

Answer 1

Răspuns:

Explicație pas cu pas:

Știind că x/y=3/4 calculați:

a) x²+y²/x²

(x/y)²=(3/4)²  ⇒x²/y²=9/16  ⇒x²=9y²/16  

(x²+y²)/x²=(9y²/16+y²)/(9y²/16)=(9y²+16y²)/16·(16/9y²)=(25y²/16)·(16/9y²)=

25y²/9y²=25/9

(x²+y²)/x²=25/9

b) 2x+5y/5x-y

x/y=3/4  ⇔x=3y/4

(2x+5y)/(5x-y)=(2·3y/4+5y)/(5·3y/4-y)=(6y/4+20y/4)/(15y/4-4y/4)=(26y/4)/(11y/4)=(26y/4)·(4/11y)=26y/11y=26/11

(2x+5y)/(5x-y)=26/11

c) 7x-2y/x+y​

x/y=3/4  ⇔x=3y/4

(7x-2y)/(x+y​)=(7·3y/4-2y)/(3y/4+y)=(21y/4-8y/4)/(3y/4+4y/4)=(13y/4)/(7y/4)=

(13y/4)·(4/7y)=13y/7y=13/7

(7x-2y)/(x+y​)=13/7