Question

if x+y+x/y=1/3 and (x+y)x/y=-1/2 then find x and y​

Answer 1

Step-by-step explanation:

let X+y=p

and x/y=q

then we have a quadratic

a²-(1/2)x-1/2 =0

(a-1)(a+1/2)=0

a=1

a=-1/2

case 1

p=1,q=-1/2

x+y=1

x/y=-1/2

y=-2x

we get

X=-1

y=2

this got rejected as y>0 here

similarly

case 2

P=-1/2

q=1

solve this to get answer

x=y=-1/4

Answer 2

Step-by-step explanation:

x+y+x/y=1/2......(i)

{y(x+y) +x}/y=1/2

{xy+y^2+x}/y=1/2

xy+y^2+x=y/2 ....... (1)

(x+y)x/y=-1/2.......(b)

(x+y) x/y=-1/2

{x^2+xy}/y=-1/2

x^2+xy=-y/2.......(2)

On adding the equation( 1 )and (2)

{xy+y^2+x}+x^2+xy=y/2-y/2

x^2+y^2+2xy+x=0

I hope this helps you

• thanks