Question

a+1/a=1 then a^3+1=??​

Answer 1

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Q If a+1/a=1 then a3=?

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Given a+1/a=1

multiply with a^2 both sides

a^3+a=a^2_______(1)

=>a(a^2+1)=a^2

=>a^2=a-1;

now from 1, a^3=a^2-1=>a^3+a=a-1=>a^3=-1

6 years agoHelpfull: Yes(23) No(8)a+1/a=1,

a^2+1=a;

a^2-a+1=0;

(a+1)(a^2-a+1)=(a+1)*0;

a^3+1=0;

a^3=-1;

6 years agoHelpfull: Yes(17) No(0)Since a+1/a=1, we can 1/a=1-a ---- assume equation (1)

Now, taking square on both side

we get

a^2 + 1/a^2 + 2=1

a^2 + 1/a^2 = -1 put the value of 1/a form equation (1)

a^2 + (1-a)^2=-1

a^2 + 1 + a^2 -2*a=-1

2*a^2 - 2*a=-2

a^2 - a =-1

a(a-1)=-1

a=-1,0

Here a=0 mean, there is no meaning

so, finally a=-1

and Answer is: a^3=-1

6 years agoHelpfull: Yes(13) No(9)a+1/a=1

a^2+1=a => a^2=a-1

a^2-a+1=0

multiplying and devide by a

a^3-a^2+a=0

a^3=a^2-a

a^3=a-1-a

a^3=-16 years agoHelpfull: Yes(4) No(3)(a+1)/a=1

(a+1)^2=a^2

a^2+2a+1=a^2

2a=-1

a=-1/2

a^3=-1/8 ans6 years agoHelpfull: Yes(3) No(7)(a+1/a)=1

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I hope that helps you