Question

Dau coroana!!!!!!!
x patrat+y patrat=290
xy=143
x,y=?

Answer 1

   
[tex]\displaystyle\\ x^2+y^2=290\\ xy=143\\ ---\\ \text{Stim ca:}\\ (x+y)^2=x^2+2xy+y^2\\ \Longrightarrow~~x^2+y^2=(x+y)^2-2xy\\ x^2+y^2=290\\ xy=143\\ ---\\ (x+y)^2-2xy=290\\ (x+y)^2=290+2xy\\ (x+y)^2=290+2\cdot 143\\ (x+y)^2=290+286\\ (x+y)^2=576\\ x+y=\sqrt{576} \\ x+y=24\\ \text{Avem ecuatiile:}\\ x+y=24\\ xy=143\\ \text{Descompunem pe 143 in factori primi:}\\ 143=11\cdot13 \Longrightarrow~~\boxed{\bf x=11~si~y=13~~sau~~ x=13~si~x=11}\\ \text{Verificam suma}\\ x+y=11+13=24~~\bf Corect[/tex]

Answer 2

sper sa înțelegi.....