The word algebra is a Latin variant of the Arabic word al-jabr

Algebra Level 2

If $\large a^{3}+\dfrac{1}{a^{3}}=3$ then which is correct for $\large a^{3}-\dfrac{1}{a^{3}}$ ?

1.It is an irrational number

2.It is a prime number

3.It is a real number

4.It is a rational number.

5.It is an integer

1,3,5 3,4 2 1,3 1

1 solution

Amit Hasan Arpon
Jan 5, 2018

let, a^3=x x+1/x=3 or, x^2-3x+1=0 so, x=(3+5^1/2)/2 or x=(3-5^1/2)/2 for first solution, x-1/x=5^1/2 for second solution, x-1/x=-5^1/2 for both cases, the result is an irrational number. It is also a real number

The word algebra is a Latin variant of the Arabic word al-jabr

1 solution

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