Question

FIE X>Y>0 SI X PATRAT +Y PATRAT =10 SI X*Y=4 CALCULATI X+Y SI X-Y

Answer 1

$xy=4 \Rightarrow 2xy=8. \\ \\ x^{2} +2xy+y ^{2} =10+8=18 = (x+y)^2 \Rightarrow x+y= \sqrt{18}=3 \sqrt{2} . \\ \\ x^{2} -2xy+y^2=10-8=2 =(x-y)^2 \Rightarrow x-y= \sqrt{2}. \\ \\ Observatie:~cazurile~cand~(x+y)~sau~(x-y)~sunt~negative~au~fost \\ ignorate~pentru~ca~x\ \textgreater \ y\ \textgreater \ 0,~ceea ~ce~inseamna~ca~(a+b)~si~(a-b)~ \\ sunt~mai~mari~decat~0.$