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x^0.5+y=7 and x+y^0.5=11 then what is the value of x,y?
x=1 y=2
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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