If $$a^3+\frac{1}{a^3}=2$$, then value of $$\frac{a^2+1}{a}$$ is (a is a positive number)
Given : $$a^3+\frac{1}{a^3}=2$$
To find : $$\frac{a^2+1}{a}=(a+\frac{1}{a}) = x = ?$$
We know that, $$(a+\frac{1}{a})^3=a^3+\frac{1}{a^3}+3(a)(\frac{1}{a})(a+\frac{1}{a})$$
=> $$(a+\frac{1}{a})^3=2+3(a+\frac{1}{a})$$
=> $$x^3=2+3x$$
=> $$x^3-3x=2$$
=> $$x(x^2-3)=2 \times 1$$
Thus, the only value that satisfy above equation is $$x=2$$
=> Ans - (B)
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