Question

If √x+y=11 and x+√y=7 Find the value of x and y ? Please reply quickly.

Answer 1

Given:

√x + y = 7

x + √y = 11

Let √x = a and √y = b

a + b² = 7 ---------- (1)

a² + b = 11 ---------- (2)

Multiply eq (1) by a² & eq (2) by a

a³ + a²b² = 7a² ---------- (3)

a³ + ab = 11a ---------- (4)

Subtract eq 4 from eq 3

a²b² – ab = 7a² – 11a

ab(ab – 1) = a(7a – 11)

[ Take ab Common from LHS & a from RHS]

b(ab – 1) = (7a – 11)

ab² – b = 7a – 11

– b = 7a – ab² – 11

– b = a(7 – b²) – 11

[ Take 'a' common from RHS]

a = (11 – b)/(7 – b²)

Let b = 1, 2, …

when b = 2

a = (11 – b)/(7 – b²)

= (11 – 2)/(7 – 4)

= 9/3 = 3

a = 3

b = 2

√x = 3 & √y = 2

[ On squaring both sides]

x= 3² & y = 2²

x = 9 and y = 4

Hope this will help you....

Answer 2

√x+y=11---------------(1)

x+√y=7---------------(2)

By observing the equations, we can say x and y are positive square numbers

Take equation (2)

As √y cannot be negative, x is a square number less than 7

Square number less than 7 is 1 and 4

Substitute x=1 in  equation (1)

=>√1+y=11

=> 1+y=11

=> y=10

The value of y cannot be 10 since it is not a square number

Substitute x=4 in equation

=> √4+y = 11

=> 2+y = 11

=> y=9

As 9 is a square number, it becomes the value of y

Answer: 
x=4 
y=9

Hope it helps