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# x^0.5+y=7    and    x+y^0.5=11                      then what is the value of x,y?

## 3 Answers

9 years ago

X1/2 + (Y1/2)2 = 11        - (1)

(X1/2)2 + Y1/2   =  7    -(2)

SUBTRACTING   (2)  FROM  (1) , WE GET

(X1/2)2  +  Y1/2  -  X1/2  - (Y1/2)2   =  4

(X1/2)2   - (Y1/2)2   +  Y1/2  -  X1/2   =  4

( (X1/2)2   - (Y1/2)2)   -  ( X1/2 - Y1/2 ) =  4

APPLYING  A2 - B2

(X1/2  +Y1/2 )(X1/2 - Y1/2 )   -  ( X1/2 - Y1/2 ) = 4

TAKING  X1/2 - Y1/2  COMMON

(X1/2 - Y1/2 ) ( X1/2  +Y1/2 -1 ) = 4

4 = 2 * 2  ,  4 = 4 * 1  AND 4 CAN'T BE EQUAL TO ANY FRACTION * FRACTION

(X1/2 - Y1/2 ) CAN'T BE EQUAL  TO 2

THERE FORE  (X1/2  +Y1/2 ) = 4 OR 1

IF ,   (X1/2 - Y1/2 )= 1 , THEN ( X1/2  +Y1/2 -1 ) WILL BE EQUAL TO INTEGER > 10

THERE FORE , (X1/2 - Y1/2 ) = 4

AND           ( X1/2  +Y1/2 -1 )  =  1

ON SOLVING WE GET    X  =  9  AND   Y  = 4

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