Question

if root x + Y equal to 11 and X + root Y is equal to 7 then find the value of x and y

Answer 1

root x + y = 11. Equation 1

root y + x = 7. Equation 2

root y = 7 - x. Square both sides

y = x^2 -14x + 49.

root x + y = 11. Substitute for y, x^2 -14x + 49

root x + x^2 -14x + 49 -11 = 0. Re-arrange.

x^2 -14x + root x + 38 = 0

Let a = root x. Then

a^4 - 14 a^2 + a + 38 = 0

True when a = 2.

a = root x = 2

Substitute root x = 2 into equation 1 which is root x + y = 11 and get y = 9

Check out solution in equation 2.

Answer x = 4 and y = 9