Question

√x/y = 24/5 + √y/x and x+y=26, then what is the value of xy?

Answer 1

Let z=✓(x/y) , then, z=24/5+1/z

z=24z+5 / 5z

5z2 - 24z - 5=0

5z2 - 25z + z - 5=0

5z (z - 5) + 1(z - 5) =0

(z - 5)(5z+1) =0

z=5 or -1/5 that is ✓(x/y) = 5 or -1/5

let consider

✓(x/y) =5

(x/y) =25

x=25y ...(i)

As is given x + y = 26

then 25y + y =26 From Eqs (i)

26y = 26

y = 1

Hence x = 25

and xy = 25 * 1 = 25