Question

x+1/x = 7
so find x^10+1/x^10

Answer 1

Answer:

If the value of x + 1/x = √13 , then what is x^5 - 1/x^5 =?

x+1x=13−−√

(x+1x)2=(13−−√)2

x2+1x2=13−2=11(1)

(x−1x)2=x2+1x2−2=11−2=9

x−1x=±3(2)

(x−1x)3=(±3)3

x3−1x3−3(x−1x)=±27

x3−1x3=±27+(3)(±3)=±36(3)

(x3−1x3)(x2+1x2)=(±36)(11)

x5−1x5+(x−1x)=±396

x5−1x5=±396∓3

x5−1x5=±393

Let me knw if any query about answer

x+1/x=(13)^1/2. Now the value of

x-1/x=[(x+1/x)^2-4]^1/2

=(13-4)^1/2=(9)^1/2

or,x-1/x=3

Again, x^4-1/x^4=(x^2+1/x^2)(x+1/x)(x-1/x)=[(x+1/x)^2-2)]×(13)^1/2×3=(13-2)×3(13)^1/2

or,x^4-1/x^4=33(13)^1/2. Now to find the value of x^5-1/x^5 we should proceed as under: (x^4-1/x^4)×(x+1/x)=x^5-1/x^3+x^3-1/x^5=x^5-1/x^5+(x^3-1/x^3)

or, x^5-1/x^5

=(x^4-1/x^4)(x+1/x)—(x^3-1/x^3)

=33×(13)^1/2×(13)^1/2–(x-1/x)(x^2+1/x^2+1).

=33×13-3(13-2+1)

=429-3×12=429–36

=393

So,x^5-1/x^5=393

Answer 2

Answer:

the rational number that is equal toit's negative is