Question #58346

1 Answer
Sep 17, 2016

x=9/2+sqrt17/2, y=-9/2+sqrt17/2x=92+172,y=92+172,

and,

x=9/2-sqrt17/2, y=-9/2-sqrt17/2x=92172,y=92172.

Explanation:

Let (x-y)^(1/2)=a :. (x-y)=a^2. Using these in the 1^(st) eqn., we

get, 3a^2+a-30=0 rArr a=-10/3,or, a=3

:. (x-y)^(1/2)=-10/3" is not admissible, since, "(x-y)^(1/2) >0.

:. (x-y)^(1/2)=3 rArr x-y=9, or, x=y+9.

By the 2^(nd) eqn., then,

(y+9)y+27=11, or, y^2+9y+16=0

:. y=(-9+-sqrt(81-64))/2=(-9+-sqrt17)/2=-9/2+-sqrt17/2.

Corresponding x=y+9=-9/2+-sqrt17/2+9=9/2+-sqrt17/2.

Thus, x=9/2+sqrt17/2, y=-9/2+sqrt17/2, and,

x=9/2-sqrt17/2, y=-9/2-sqrt17/2.

These roots satisfy the eqns. Hence, the soln.