Question

Please answer my question.


-Brainly​

Answer 1

Answer:

47

Step-by-step explanation:

x^2 + 1/x^2 = (X + 1/X)^2 - 2 = 7^2 - 2

x^2 + 1/x^2 = 47

Now

x^3 + 1/x^3 = (X + 1/x)^3 - 3(x + 1/X) =343 - 21

x^3 + 1/x^3 = 322

Now

x^6 + 1/x^6 = (X^3 + 1/x^3)^2 - 2

x^6 + 1/x^6 = 322*322 - 2

x^6 + 1/x^6 = 103682

Answer 2

Answer: 322 and 103682

Step-by-step explanation:

(i)

$x+\frac{1}{x}=7.....(i)\\=>(x+\frac{1}{x})^2=7^2\\=>x^2+(\frac{1}{x})^2+2(x)\frac{1}{x}=49\\=>x^2+\frac{1}{x^2}+2=49\\\\=>x^2+\frac{1}{x^2}=47..........(ii)\\\\\\\\Now, Multiplying(i)with(ii)\\we\;get\\(x+\frac{1}{x})(x^2+\frac{1}{x^2})=7\times47\\\\=>x^3+x+\frac{1}{x}+\frac{1}{x^3}=329\\=>x^3+\frac{1}{x^3}+(x+\frac{1}{x})=329\\\\=>x^3+\frac{1}{x^3}=329-7=322....Ans(i)\\\\\\\\Now,\\(x^3+\frac{1}{x^3})^2=103684\\\\=>x^6+\frac{1}{x^6}+2(x^6)(\frac{1}{x^6})=103684 \\\\=>x^6+\frac{1}{x^6}=103684-2$

=103682

$Learning\;\;together\;:)$