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CBSE Class 9 Answered

If x to the power of 4 plus 1 over x to the power of 4 equals 194 comma space t h e n space x cubed plus 1 over x cubed=
Asked by dhanya_mk2000 | 01 Jan, 2020, 07:59: PM
answered-by-expert Expert Answer
x⁴ + (1/x⁴) = 194

Now, ( x² + (1/x²) )² - 2 =x⁴ + (1 / x⁴)
 
therefore,
( x² + (1/x²) )² - 2 = 194
( x² + (1/x²) )² = 194+2
x² + 1/x² = √196
x² + 1/x² = 14 

using, ( x + (1/x) )² - 2 = x² + 1/x² 

( x + 1/x )² - 2 = 14
( x + 1/x )² = 14 +2
( x + 1/x ) =√16
x + 1/x = 4
 
 
Therefore,
x³ + 1 / x³ = ( x + 1/x )([x² + 1/x²] - 1 )
= 4 × ( 14 - 1 )
= 4 × 13 
= 52
Answered by Arun | 02 Jan, 2020, 12:57: PM

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