could anyone please find out the X and Y in the following SIMULTANEUSE EQUATION: √X +Y=7 AND X+√Y=11?

Question

√X +Y=7
X+√Y=11

Answer 1

above has got it!

Answer 2

There aren't very many possibilities if X and Y are whole numbers, and they must also be perfect squares, otherwise their square roots would stop one equation or the other from being correct. And in the first equation, Y = 1 and Y = 4 are the only possibilities for which √X is positive. Trying Y = 1 gives √X = 6 from the first equation, and 36 + 1 = 11 in the second equation, which is wrong. Trying Y = 4 gives √X = 3 from the first equation, and 9 + 2 = 11 in the second equation, which is right - which is just as well, because there was nothing else to try.

Answer 3

X = 9 and Y = 4

Answer 4

From √X +Y=7 you have x=(7-y)^2 (I)
From X+√Y=11 you get y=121-22x+x^2 (II)
Substituing x from (I) in (II)
y=121-22*(7-y)^2+(7-y)^4 or rearranging
114 +7-y-22*(7-y)^2+(7-y)^4 =0 replacing (7-y) by v you get
114+v-22*v^2+v^4=0 factoring it you get (v-3)(v^3+3v^2-13v-38)=0
the v=3, but v=3=7-y and y=4 and from (II) x=9
That´s all.

Answer 5

here's an iteration method for this
type of problem-in order to get
an accurate answer,reiterate
until it converges to the number of
decimal places required

sqrtx+y = 7........(1)
x+sqrt y= 11..........(2)

from (1),y=7-sqrtx

substitute into (2)

x+sqrt{7-(sqrtx)}=11
>>>x=11-sqrt{(7-sqrtx)}

we now have the iteration

x1=a good guess

x(n+1)=11-sqrt{7-sqrtx(n)}
for n=1,2,3,..........

(take the +ve values of the sqrts)

try x1=6
x2=8.866807496
x3=8.986088249
x4=8.999420204
x5=8.999977582
x6=9 (damn near it)

substitute into (1) to get y=4

it's a waste of time trying to break down
these type of problems with algebra-the
equations are too long to deal with
there are four roots in a quartic-they don't
have to be equal or real-if one iteration
diverges,another can be tried to get the
real root(s)

other prob
(take+ve roots)

x1=8,
x(n+1)=10-sqrt{5-sqrtx(n)}
n=1,2,3...........
x2=8.526374242
x3=8.557777853
x4=8.559641705
x5=8.559752291
x6=8.559758852
x7=8.559759241

substitute into first equation for x
y=2.074293377
these numbers are near enough-the
'error' is 1 in10^7(approx)
this method will work with surds or
integers in the answer

thanks for the probs

i hope that this helps

Answer 6

X = 9
Y = 4

Answer 7

x=9
y=4

Answer 8

x=9
y=4

Answer 9

I think they've got it