Question

Determinati nomerele x si y stiind ca :

A. Sunt invers proportionale cu 3 si 4, iar x-y=63 ;
B. Sunt invers proportionale cu 2 si 3, iar x la putere 2 + y la puterea 2 = 208..

Answer 1

vezi daca intelegi
a) x/1/3=y/1/4⇔x:1/3=y:1/4⇔x×3=y×4⇒x=y×4/3
x-y=63 dar am aflat ca x=y×4/3 si inlocuim
4y/3-y=63 aduc la acelasi numitor
4y/3-3y/3=63
y/3-63⇒y=63×3⇒y=189
acum avem x-y=63 si y=189 inlocuim
x-189=63
x=63+189
x=252
b) x/1/2=y/1/3⇔x:1/2=y:1/3⇔2x=3y⇒x=3y/2
x²+y²=208 
daca x=3y/2⇒x²=(3y/2)²⇒x²=9y²/4
acum avem x²+y²=208 si x²=9y²/4 inlocuim
9y²/4+y²=208  aduc la acelasi numitor
9y²/4+4y²/4=208
13y²/4=208⇒13y²=208×4⇒13y²=832⇒y²=832:13⇒y²=64⇒y=√64⇒y=8
acum avem y=8 si y²=64 iar x²+y²=208 inlocuim
                                          x²+64=208⇒x²=208-64⇒x=144⇒x=√144⇒x=12

Answer 2

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