Question

Va rog mult. Va dau maximul de puncte
1.Stiind ca x+y=7 si x*y=12 aflati:
a)x²+y²
b)x²-y²
c)x-y
2.Stiind ca x-y=3 si x²+y²=29 aflati:
a)x*y
b)x+y
c)x²-y2

Answer 1

[tex]x+y=7 \\ xy=12 \\ a)x^2+y^2 \\ b)x^2-y^2 \\ c)x-y \\ ------- \\ a)(x+y)^2=x^2+y^2+2xy \\ 49=x^2+y^2+24 \\ \boxed{x^2+y^2=25} \\ b)x*y=12 \\ Daca~x=1~si~y=12 \Longrightarrow x+y \neq 7 \\ Daca~x=4~si~y=3 \Longrightarrow x+y=7 => x=4~si~y=3 \\ x^2-y^2=4^2-3^2 \\ \boxed{x^2-y^2=5} \\ c)x-y=4-3 \\ \boxed{x-y=1}[/tex]


[tex]x-y=3 \\ x^2+y^2=29 \\ a)xy \\ b)x+y \\ c)x^2-y^2 \\ ------- \\ a)(x-y)^2=x^2+y^2-2xy \\ 9=29-2xy \\ 2xy=20 \\ \boxed{xy=10} \\ b)x*y=10 \\ Daca~x=1~si~y=10 \Longrightarrow x-y \neq 3 \\ Daca~x=5~si~y=2 \Longrightarrow x-y=3~deci~x=5~si~y=2 \\ x+y=5+2 \\ \boxed{x+y=7} \\ c)x^2-y^2=5^2-2^2 \\ \boxed{x^2-y^2=21}[/tex]