Question

If xy = 2 and x^2 + y^2 = 5, then x/y + y/x =

Answer 1

5/2

Answer 2

x/y +y/x = x^2 + y^2 /xy = 5 / 2 (From given equaions)

Answer 3

thanks thanks ..

Answer 4

if you like some solution...

xy = 2 so.. x = 2/y

x^2 + y^2 = 5 so... x = sqrt (5 - y^2)

x = x so... 2/y = sqrt 95-y^2) square both sides...

4/y^2 = 5 - y^2

multiply everything by y^2 to bring it on top...

4 = 5y^2 - y^4

y^4 - 5y^2 + 4 = 0

let a = y^2

a^2 - 5a + 4 = 0

(a-1)(a-4) = 0
a = 1; 4

y^2 = 1, 4
y = 1, - 1, 2, -2

xy = 2

if y = 1..x = 2
y = -1 x = -2
y = 2..x = 4
y = -2 x = -4

so...
x/y + y/x = 2/1 + 1/2 = 4/2 = 1/2 = 5/2

(it is the same for all values of x and y)

Answer 5

that las one was 4/2 + 1/2 = 5/2