Răspuns :
[tex]Este: x^{3} + \frac{1}{ x^{3}} sau \frac{ x^{3}+1 }{ x^{3}} ???[/tex]
Ai ales prima varianta si ai spus ca
[tex] x^{3} + \frac{1}{ x^{3} } = 4[/tex]
Aducem la acelasi numitor:
x³ + 1 = 4x³
4x³ - x³ = 1
3x³ = 1
x³ = 1/3
[tex]x = \sqrt[3]{ \frac{1}{3} } = \frac{1}{ \sqrt[3]{3} } = \frac{ \sqrt[3]{ 3^{2} } }{3} = \frac{ \sqrt[3]{9} }{3} [/tex]
Ai ales prima varianta si ai spus ca
[tex] x^{3} + \frac{1}{ x^{3} } = 4[/tex]
Aducem la acelasi numitor:
x³ + 1 = 4x³
4x³ - x³ = 1
3x³ = 1
x³ = 1/3
[tex]x = \sqrt[3]{ \frac{1}{3} } = \frac{1}{ \sqrt[3]{3} } = \frac{ \sqrt[3]{ 3^{2} } }{3} = \frac{ \sqrt[3]{9} }{3} [/tex]
(x+1)/x=4 <=> x/x +1/x =4
x/x + 1/x=4
1+1/x=4
1/x=4-1
1/x=3
x=3
x³ + 1/x³= 3³ + 1/3³= 27 + 1/27 aducem la acelasi numitor
(729+1)/27= 730/27
x/x + 1/x=4
1+1/x=4
1/x=4-1
1/x=3
x=3
x³ + 1/x³= 3³ + 1/3³= 27 + 1/27 aducem la acelasi numitor
(729+1)/27= 730/27