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Serzic711
@Serzic711
August 2022
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Известно что (x+1/x)скобка в квадрате=3. Найдите x в кубе + 1/x в кубе
(1/x дробь)
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oganesbagoyan
Verified answer
Task/25870381
-------------------
(x +1/x)² =3
---------------
* * * a³+b³ =(a+b)³ -3ab(a+b) * * *
x³ +(1/x)²=(x+1/x)³ -3x*(1/x)*( x+1/x) =(x+1/x)³ -3( x+1/x)=3³ -3*3 =18.
ответ : 18.
--------------P.S. -----------
(a+b)³ =a³ +3a²b +3ab²+b³ =
a³ +b³
+3ab(a+b) ;
a³ +b³ = (a+b)³ - 3ab(a+b) =
* * * =(a+b) ( (a+b)² -3ab) =(a+b) (a²+2ab+b² -3ab) =(a+b)((a²- ab+b²) * * *
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Serzic711
А p.s надо писать?
oganesbagoyan
НЕТ дальше пояснение
Serzic711
Спасибо
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Answers & Comments
Verified answer
Task/25870381-------------------
(x +1/x)² =3
---------------
* * * a³+b³ =(a+b)³ -3ab(a+b) * * *
x³ +(1/x)²=(x+1/x)³ -3x*(1/x)*( x+1/x) =(x+1/x)³ -3( x+1/x)=3³ -3*3 =18.
ответ : 18.
--------------P.S. -----------
(a+b)³ =a³ +3a²b +3ab²+b³ = a³ +b³ +3ab(a+b) ;
a³ +b³ = (a+b)³ - 3ab(a+b) =
* * * =(a+b) ( (a+b)² -3ab) =(a+b) (a²+2ab+b² -3ab) =(a+b)((a²- ab+b²) * * *