Question

x+1/x=3 then find the value of x^6+1/x^6 =?​

Answer 1

Answer:

Step-by-step explanation:

It is given that :-

$\rm{x + \dfrac{1}{x} = 3}$

We need to find the value of :-

$\sf{x^6 + \dfrac{1}{x^6}}$

For this, we need to use the following identities :-

$\rm{a^2 + b^2 = (a+b)^2 - 2ab}$

And, we need to use this one as well :-

$\rm{a^3 + b^3 = (a+b) (a^2 - ab + b^2)}$

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

322 is the required answer. Refer to Attachment for the solution.

Answer 2

Answer:

$\huge\bf\maltese{\underline{\red{Answer ࿐}}}\maltese$

$x \: + \frac{1}{3} = 3$

squaring both side we have

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

$x^{2} + \frac{1}{x ^{2} } + 2 = 9$

$x^{2} + \frac{1}{x^{2} } = 9 - 2$

$x ^{2} + \frac{1}{x ^{2} } = 7 \: \: \: \: \: ...(1)$

cubing equation (1) both sides,

$= (x ^{2} + \frac{1}{x^{2} }) ^{3} = (7) ^{3}$

$= x ^{6} + \frac{1}{x^{6} } + 3(x^{2} + \frac{1}{x^{2} }) = 343$

$= x ^{6} + \frac{1}{x^{6} } + 3 \times 7 = 343$

$= x ^{6} + \frac{1}{x^{6} } = 322$

therefore answer is 322