Question

If x^3=26+15√3, then show that x + 1/x is a rational number

Answer 1

Answer:

the answer is 1

Step-by-step explanation:

u can check it out

Answer 2

Answer:

x + 1/x = 4.... it is a rational number

Step-by-step explanation:

x = 26+15√3 = 8 + 12√3+ 18 + 3√3

=2^3+ 3.2^2.√3+3.2.(√3)^2+(√3)^3

=(2+√3)^3

So ,hereby x = 2+√3

so now as per the question

x + 1/x

= ($\frac{(2+\sqrt{3})^2 + 1 }{2+\sqrt{3} }$

=  $\frac{8+ 4\sqrt{3} }{2+ \sqrt{3} }$

= 4

and 4 is a rational number