squa root x +y =11 x + square root of y = 7 find x and y

Hello keshav..!

root(x) + y = 11  = > root(x) = 11 - y -----(1)

and root(y) + x = 7  => x = 7 - root(y ) ----(2)

Hence from one and two ..   root ( 7 - root(y) = (11-y)

Sqaure both side ..  7 - root(y) = y^2 + 121 - 22y

y^2 -22y +root(y) + 114 = 0

Let root(y) = z

z^4 - 22z^2 + z + 114 = 0----(4)

Now by randomly guessing z = 1 , 2 , 3 we get that z = 3 will satisfy the equation ..

z=3 is one solution ...

Hence root(y) =3   or  y = 9   and x = 4

Divide the expression (4) by (z-3) ..you will get anothe cubic polynomial ..check whether any value of z satisfy it or not..if yes then ..calculate it...correspodingly you will get another value of x nd y ..

And if not the single solution ..(9,4)   [Do the rest part ..don't leave it ..Ok ! ]

Regrads

Yagya

Approved