if x2 plus 1/x sqaure = 62 find value of x3 plus 1/x3

Asked by cute_ridhhi18 | 14th Aug, 2015, 07:29: PM

Expert Answer:

G i v e n space t h a t space x squared plus 1 over x squared equals 62 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 cubed plus 1 over x cubed colon x squared plus 1 over x squared equals 62 rightwards double arrow x squared plus 1 over x squared plus 2 equals 62 plus 2 rightwards double arrow x squared plus 1 over x squared plus 2 x cross times 1 over x equals 64 rightwards double arrow open parentheses x plus 1 over x close parentheses squared equals 8 squared rightwards double arrow open parentheses x plus 1 over x close parentheses equals 8... left parenthesis 1 right parenthesis  A g a i n space 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 colon space x squared plus 1 over x squared equals 62 rightwards double arrow x squared plus 1 over x squared minus 1 equals 62 minus 1 rightwards double arrow x squared plus 1 over x squared minus 1 equals 61... left parenthesis 2 right parenthesis  W e space k n o w space t h a t a cubed plus b cubed equals open parentheses a plus b close parentheses open parentheses a squared minus a b plus b squared close parentheses therefore x cubed plus 1 over x cubed equals open parentheses x plus 1 over x close parentheses open parentheses x squared plus 1 over x squared minus x cross times 1 over x close parentheses equals open parentheses x plus 1 over x close parentheses open parentheses x squared plus 1 over x squared minus 1 close parentheses T h u s comma space x cubed plus 1 over x cubed equals 8 cross times 61 space....... open square brackets f r o m space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis close square brackets rightwards double arrow x cubed plus 1 over x cubed equals 488

Answered by Vimala Ramamurthy | 16th Aug, 2015, 09:04: AM

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