Question

Please help. What is the greatest positive value for y in the system: x^2 + y^2 = 5 & xy = 2

Answer 1

u wana use calculus/graphing ?

Answer 2

you can also use lagrange ,if you are familiar with it

Answer 3

does it matter wich one you maximise and which one is your constraint

Answer 4

we can say y=2/x
put in the eq

Answer 5

u get a new eq solve for it u get the result

Answer 6

i think the geometric approach is quite obvious,the functions are are already given,the question wud be what is the highest value of y when a circle of radius sqrt{5} intersect with hyperbola,which is pbviously the intersection

Answer 7

just an alternative

x = 2/y

(2/y)^2 + y^2 = 5
4/y^2 + y^2 = 5
4 + y^4 = 5y^2
y^4 - 5y^2 + 4 = 0
(y^2 - 1)(y^2 - 4) = 0
(y+1)(y-1)(y+2)(y-2) = 0
make each factor equals zero, then solve for y

Answer 8

So what would be the exact answer? :O

Answer 9

@RadEn is finding the intersection ,so we really dont need maximising ,just point P,as it is evidently the highest value of y

Answer 10

yes just solving the equations wil do lol

Answer 11

got it. Highest value is 2. SS is (1,-1,2,-2) Thanks!

Answer 12

yes, calculus wud work if some function \(f(x,y)=x^2+y^2\) with \(xy=2\) as constraint
2 is the highest value,

Answer 13

thanks!