Question

Solve the system of equation:

root x + y = 11 ,&
x + root y = 7


for real values of x, and y?

PLEASE DON'T SEND SOLUTION, I ALREADY KNOW THE SOLUTION THAT
x = 4
y = 9

ONLY SEND PROCESS!!!
IF YOU KNOW.......

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Answer 1

Step-by-step explanation:

√x+y=11

x+√y= 7

from eq 1...

from eq 1...√y=7-x

from eq 1...√y=7-xy=(7-x)^2

from eq 1...√y=7-xy=(7-x)^2from eq 2...

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-y

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sides

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401x^4-28x^3+272x^2-1065x+1444=0

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401x^4-28x^3+272x^2-1065x+1444=0from the rational root theorem, possible roots are factors of 1444

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401x^4-28x^3+272x^2-1065x+1444=0from the rational root theorem, possible roots are factors of 14444 is a factor of 1444 and a root of the equation...

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401x^4-28x^3+272x^2-1065x+1444=0from the rational root theorem, possible roots are factors of 14444 is a factor of 1444 and a root of the equation...256-1792+4352-4260+1444=0

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401x^4-28x^3+272x^2-1065x+1444=0from the rational root theorem, possible roots are factors of 14444 is a factor of 1444 and a root of the equation...256-1792+4352-4260+1444=0-1536+4352-4260+1444=0

from eq 1...√y=7-xy=(7-x)^2from eq 2...√x=11-ysubstitute (7-x)^2 for y√x=11-(7-x)^2square both sidesx=121-22(7-x)^2+(7-x)^4(7-x)^4=(x-7)^2*(x-7)^2=(x^2-14x+49)(x^2-14x-49)=x^4-28x^3+294x^2-1372x+2401x=121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+24010=-x+121-22x^2+308x-1078+x^4-28x^3+294x^2-1372x+2401x^4-28x^3+272x^2-1065x+1444=0from the rational root theorem, possible roots are factors of 14444 is a factor of 1444 and a root of the equation...256-1792+4352-4260+1444=0-1536+4352-4260+1444=02816-4260+1444=0.

-1444+1444=0

-1444+1444=00=0

[Solved..]