Question

If x= 4-√15 find (1) x^2+1/x^2
(2) x^4+1/x^4

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

x= 4-√15

1/x = 1/4-√15

Rationalise the dinominator

You will get

1/x = 4 + √15

x² = ( 4 -√15 )²= 16 + 15 -8√15

                       = 31 - 8√15

1/x² = ( 4+ √15 )² = 16 + 15 + 8√15

                           = 31 + 8√15

therefore

x² + 1/x² = 31 -8√15 + 31 + 8√15

             = 31 +31=62

( 2 )

(x²+1/x²)² = x∧4 + 1/x∧4 + 2

62² = x∧4+ 1/x∧4 + 2

3844 -2 = x∧4 +1/x∧4  =  3842