Question

si: x+1/x= 3 hallar: x^3+1/x^3​

Answer 1

SOLUCIÓN

♛ HØlα!! ✌

⚠ Recordemos que

                $\boxed{\boldsymbol{(a+b)^3 = a^3 +b^3+3ab(a+b)}}$

Entonces

                                     $x+\dfrac{1}{x} = 3\\\\\\\left(x+\dfrac{1}{x}\right)^3 = (3)^3\\\\\\x^3+\left(\dfrac{1}{x}\right)^3+3\underbrace{(x)\left(\dfrac{1}{x}\right)}_{1}\underbrace{\left(x+\dfrac{1}{x}\right)}_{3}=3^3\\\\\\x^3+\dfrac{1}{x^3}+ 3(1)(3) = 3^3\\\\\\x^3+\dfrac{1}{x^3}+ 9 = 27\\\\\\\boxed{\boxed{\boldsymbol{x^3+\dfrac{1}{x^3}= 18}}}$