Question

If x = 3 - √8 find x³ + 1 ÷ x³ (x³ is divided by 1 alone )

Answer 1

3-root8+ 1/3-root8 ×3+root8 / 3+root 8
So
3-root8+(3+root8) /(3)^2-(root8)^2
3-root8+3+root8/9-8
If we see root 8 root 8 will be cancel
6/1 =x
So
6^3is 216 so x=216
Plz mark as brainlist

dude if it is wrong plz tell me the answer

Answer 2

Hey Mate !

Here is your solution :

Given,

=> x = 3 - √8

=> x = 3 - √( 2 × 2 × 2 )

=> x = 3 - 2√2 -------- ( 2 )

Now,

= x³ + ( 1/x³ )

= { x + ( 1/x ) } { x² + ( 1/x² ) - x ( 1/x ) }

= { x + ( 1/x ) } { x² + 1/x² - 1 } -------- ( 1 )

Now,

=> x = 3 - 2√2

=> 1/x = 1 ÷ ( 3 - 2√2 )

By multiplying ( 3 + 2√2 ) in numerator and denominator of R.H.S ,

=> 1/x = 1( 3 + 2√2 ) ÷ ( 3 - 2√2 ) ( 3 + 2√2)

=> 1/x = ( 3 + 2√2 ) ÷ [ ( 3 )² - ( 2√2 )² ]

=> 1/x = ( 3 + 2√2 ) ÷ ( 9 - 8 )

=> 1/x = ( 3 + 2√2 ) --------- ( 3 )

Now,

=> { x + ( 1/x ) }² = x² + ( 1/x² ) + 2 × x × ( 1/x )

=> { 3 - 2√2 + 3 + 2√2 }² = x²+( 1/x² ) + 2

=> ( 9 )² - 2 = x²+( 1/ x² )

=> 81 - 2 = x²+ ( 1/ x² )

=> 79 = x²+ ( 1/ x² ) -------- ( 4 )

Now,

By substituting the value of ( 2 ) , ( 3 ) , ( 4 ) in ( 1 ).

= { 3 - 2√2 + 3 + 2√2 ) ( 79 - 1 )

= ( 6 ) 78

= 468

The required answer is 468.

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Hope it helps !! ^_^