Elitmus
Exam
Numerical Ability
Number System
Q If a+1/a=1 then a3=?
Read Solution (Total 9)
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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
- 9 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;
- 9 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
- 9 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=-1 - 9 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 ans - 9 years agoHelpfull: Yes(3) No(7)
- (a+1/a)=1
multiplying both side by (a-1/a)
(a+1/a)(a-1/a)=(a-1/a)
a^2-1/a^2=a-1/a
a^2-a=1/a^2-1/a
a(a-1)=1/a^2(1-a)
a^3(a-1)=(-1)(a-1)
a^3= -1 - 7 years agoHelpfull: Yes(2) No(0)
- it's undetermined.......
- 9 years agoHelpfull: Yes(1) No(5)
- a+1/a=1
=> a^2 +1=a
=> a^2=a-1 .......(1)
=> a^3=a^2-a
=> a^3=a-1-a
=> a^3= - 1 .....ans
- 9 years agoHelpfull: Yes(0) No(1)
- given that
a+(1/a)=1 multiply by a^2 on both sides then
a^3+a=a^2 ...............1
a(a^2+1)=a^2
a^2+1=a
a^2=a-1
from eq 1
a^3+a=a^2
a^3=a^2-a
a^3=a-1-a
a^3=-1
- 9 years agoHelpfull: Yes(0) No(2)
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