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OLEGan [10]
4 years ago
15

If (x + 1/x)^2 = 3 what is the value of x^3 + 1/x^3

Mathematics
1 answer:
Anika [276]4 years ago
3 0

(x + 1/x)² = 3                 | √

<u>x + 1/x</u> = √3

According to short multiplication formula:

(a + b)³ =a³ + 3a²b + 3ab² + b³

x³ + 1/x³ = (x)³ + (1/x)³ = (x + 1/x)³ - 3x²/x - 3x/x² =

=  (x + 1/x)³ - 3x - 3/x = (<u>x + 1/x</u>)³ - 3(<u>x + 1/x</u>) =

= (√3)³ - 3√3 = 3√3 - 3√3 = 0

If (x + 1/x)² = 3 the value of x³ + 1/x³ is 0.

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