Question

x + 1/x = 7
x^3 + 1/x^3 = ?

$x + \frac{1}{x} = 7 \\x^{3} + \frac{1}{x^{3}} = ?$

Answer 1

Ответ:

$x^3+\dfrac{1}{x^3}= 322.$

Пошаговое объяснение:

$x^3+\dfrac{1}{x^3} = \bigg(x+\dfrac{1}{x}\bigg)\bigg(x^2-1+\dfrac{1}{x^2}\bigg)= \bigg(x+\dfrac{1}{x}\bigg)\bigg(x^2+2+\dfrac{1}{x^2}-3\bigg) = \bigg(x+\dfrac{1}{x}\bigg)\bigg(\bigg(x+\dfrac{1}{x}\bigg)^2-3\bigg) = 7(7^2-3)=7(49-3)=7*46=322.$

Answer 2

Ответ:      x³ + 1/x³ = 322 .

Пошаговое объяснение:

x + 1/x = 7

x³ + 1/x³ = ?

( x + 1/x )³ = x³ + 3x² * 1/x + 3x *( 1/x) ² + ( 1/x )³ = x³ + 3x + 3 * 1/x + 1 /x³ =

= ( x³ + 1/x³ ) + 3 ( x + 1/x ) ;

x³ + 1/x³ = ( x + 1/x )³ - 3( x + 1/x ) = 7³ - 3 * 7 = 343 - 21 = 322 .