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\sqrt{x}+y=3,\:x+\sqrt{y}=5

Asked by twishasrivastava65 9th May 2016, 2:43 PM
Answered by Expert
Answer:
C o n s i d e r space t h e space g i v e n space e q u a t i o n s
square root of x plus y equals 3 space space... left parenthesis 1 right parenthesis
x plus square root of y equals 5 space space... left parenthesis 2 right parenthesis

N o w space l e t space u s space a s s u m e space t h a t comma space x equals t squared rightwards double arrow square root of x equals t
y equals s squared rightwards double arrow square root of y equals s

T h u s space t h e space s y s t e m space o f space e q u a t i o n s space b e c o m e s
t plus s squared equals 3 space space space... left parenthesis 3 right parenthesis
t squared plus s equals 5 space space space... left parenthesis 4 right parenthesis

F r o m space e q u a t i o n space left parenthesis 4 right parenthesis comma space w e space h a v e comma space s equals 5 minus t squared space space space... left parenthesis 5 right parenthesis
S u b s t i t u t i n g space t h e space v a l u e space o f space s space f r o m space e q u a t i o n space left parenthesis 5 right parenthesis space i n space e q u a t i o n comma space left parenthesis 3 right parenthesis comma space w e space h a v e comma
t plus open parentheses 5 minus t squared close parentheses squared equals 3
rightwards double arrow t plus 25 minus 10 t squared plus t to the power of 4 equals 3
rightwards double arrow t to the power of 4 minus 10 t squared plus t plus 25 minus 3 equals 0
rightwards double arrow t to the power of 4 minus 10 t squared plus t plus 22 equals 0
L e t space u s space s o l v e space t h i s space b i q u a d r a t i c space e q u a t i o n space b y space t r i a l space a n d space e r r o r space m e t h o d.
T h u s comma space t equals 2 space i s space a space s o l u t i o n space o f space t h e space a b o v e space e q u a t i o n.
T h e space o t h e r space t w o space r o o t s space a r e space n e g a t i v e space a n d space h e n c e space w e space c a n space d i s c a r d space t h o s e space r o o t s space b e c a u s e comma space s q u a r e space r o o t space o f space a space n e g a t i v e space n u m b e r
d o e s space n o t space e x i s t s.
T h e space f o u r t h space r o o t space o f space t h e space a b o v e space e q u a t i o n space i s space a n space i r r a t i o n a l space r o o t space a n d space w e space c a n space d i s c a r d space t h a t space a l s o.

I f space t equals 2 comma space x equals t squared rightwards double arrow x equals 4
S u b s t i t u t i n g space t h e space v a l u e space space t equals 2 space i n space e q u a t i o n space left parenthesis 4 right parenthesis comma space w e space h a v e comma
t squared plus s equals 5 space space
rightwards double arrow 4 plus s equals 5
rightwards double arrow s equals 5 minus 4 equals 1

T h u s comma space y equals 1 squared equals 1

H e n c e space t h e space s o l u t i o n space i s space x equals 4 comma space y equals 1 space
Answered by Expert 10th May 2016, 9:15 AM
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