Question

Root x + y = 7
root y + x = 11

Answer 1

Your question is quite incomplete but the solution:
x+√y=11... .[.1 ] . 

√x+y= 7.......[2] . 

from equation [1] √y=11--x .so y= 121--22x+x^2 

we can substititute this value of y in equation[2] 

√x +121 --22x+x^2=7 

√x = --121+-22x--x^2+7 


solving irt by trial & error method 

if WE HAVE x==9 
THEN, WE HAVE LHS=√x==√9==3..............[A] 

& RHS=-121 +[22X9]--81= -121 +198 -81= 3...[B] 
COMPARING BOTH QUANTITITIES 
WE FIND LHS=RHS 

HENCE x=9 is the correct solution 

Now we can have y=7--√x= 7--√9=7--3=4 

hence the required value 
0f x=9 
& y=4

Hope this helps

Answer 2

Answer:

Short Method.

Step-by-step explanation:

x+√y=11 -- (i )

√x+y=7 -- (ii)

समी॰ (i) - (ii)

x+√y=11

√x+y=7

-__-__-__

x-√x+√y-y=4

x-y-√x+√y=4

(√x)^2-(√y)^2-√x+√y=1×4

(√x+√y) (√x-√y) -1 (√x-√y)=4

(√x-√y) (√x+√y-1) = 4

√x-√y= 1 --(iii)

√x+√y-1=4

√x+√y=4+1

√x√y=5 --(iv)

समी॰ (iii) + (iv)

√x+√y=5

√x-√y=1

________

2√x = 6

√x=6/2

√x=3

x=3^2

x=9

Putting x=9

y=4 Ans.

By- Raj Kumar (Math Teacher)

Mobile- 09135574303