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CBSE - VIII - Mathematics - Algebraic Expressions and Identities

1)Find the continued product:
i) (x+1)(x-1)(x2+1)
ii) (x-3)(x+3)(x2+9)
2)If x + y = 12,find the value of (x2 + y2)
3)if(x+1/x)=4,find the value of 
i)(x2 + 1/x2)
 

Asked by feeroz 8th May 2016, 7:33 PM
Answered by Expert

Answer:

1.
C o n s i d e r space t h e space g i v e n space e x p r e s s i o n colon
open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses open parentheses x squared plus 1 close parentheses
W e space k n o w space t h a t space open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared
H e r e space a equals x space a n d space b equals 1
therefore open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses equals x squared minus 1 squared equals x squared minus 1
therefore open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses open parentheses x squared plus 1 close parentheses equals open parentheses x squared minus 1 close parentheses open parentheses x squared plus 1 close parentheses
H e r e space a equals x squared space a n d space b equals 1
A g a i n space a p p l y i n g space t h e space s a m e space i d e n t i t y comma space w e space h a v e comma
open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses open parentheses x squared plus 1 close parentheses equals open parentheses open parentheses x squared close parentheses squared minus 1 squared close parentheses equals x to the power of 4 minus 1

2.
G i v e n space t h a t space x plus y equals 12 space space space space space space... left parenthesis 1 right parenthesis
W e space n e e d space t o space f i n d space t h e v a l u e space x squared plus y squared colon
S q u a r i n g space t h e space e q u a t i o n space left parenthesis 1 right parenthesis space o n space b o t h space t h e space s i d e s comma space w e space h a v e comma
open parentheses x plus y close parentheses squared equals 12 squared space space space space space space space space space... left parenthesis 2 right parenthesis
W E space k n o w space t h a t space open parentheses a plus b close parentheses squared equals a squared plus 2 a b plus b squared
H e r e comma space a equals x space a n d space b equals y
T h e r e f o r e comma space open parentheses x plus y close parentheses squared equals x squared plus 2 x y plus y squared space space space space.. left parenthesis 3 right parenthesis
T h u s comma space 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 open parentheses x plus y close parentheses squared space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis space i n space e q u a t i o n space left parenthesis 3 right parenthesis comma space w e space h a v e comma
12 squared equals x squared plus 2 x y plus y squared space
rightwards double arrow x squared plus 2 x y plus y squared space equals 144
rightwards double arrow x squared plus y squared space equals 144 space minus 2 x y
W i t h o u t space k n o w i n g space t h e space v a l u e space o f space x y comma space i t space w i l l space b e space d i f f i c u l t space t o space f i n d space t h e space v a l u e space o f space x squared plus y squared
P l e a s e space c h e c k space t h e space q u e s t i o n

3.
G i v e n space t h a t space open parentheses x plus 1 over x close parentheses equals 4
W E space n e e d space t o space f i n d space t h e space v a l u e space o f space x squared plus 1 over x squared colon
W E space k n o w space t h a t space open parentheses a plus b close parentheses squared equals a squared plus 2 a b plus b squared
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 space open parentheses x plus 1 over x close parentheses equals 4
S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma
open parentheses x plus 1 over x close parentheses squared equals 4 squared
rightwards double arrow x squared plus 1 over x squared plus 2 x cross times 1 over x equals 16 space space space open square brackets a p p l y i n g space t h e space a b o v e space i d e n t i t y close square brackets
rightwards double arrow x squared plus 1 over x squared plus 2 equals 16
rightwards double arrow x squared plus 1 over x squared equals 16 minus 2
rightwards double arrow x squared plus 1 over x squared equals 14
Answered by Expert 8th May 2016, 10:15 PM

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