The equation $x+\dfrac{1}{x}=3\;(x
eq 0)$ is expressed as a quadra...

Question

The equation $x+\dfrac{1}{x}=3\;(x
eq 0)$ is expressed as a quadratic equation in the form of $ax^{2}+bx+c=0$. The value of $a-b+c$ is :

Accepted Answer

Step 1: Multiply both sides of $x+\dfrac{1}{x}=3$ by $x$ (since $x
eq 0$).
$$x^{2}+1=3x$$
Step 2: Bring all terms to one side to get standard form.
$$x^{2}-3x+1=0$$
Step 3: Compare with $ax^{2}+bx+c=0$, so $a=1,\; b=-3,\; c=1$.
Step 4: Compute $a-b+c$.
$$a-b+c=1-(-3)+1=1+3+1=5$$
Correct option is (A) 5.

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