Question

Solve x + 1/x = 3, where x not equal to zero.

Answer 1

$x + \frac{1}{x} = 3 \\ => \frac{ {x}^{2} + 1 }{x} =3 \\ => {x}^{2} + 1 = 3 \times x \\ => {x}^{2} + 1 - 3x = 0$

Now we have to use some formulas!

We have to use discriminant method.

Arranging the equation:-

${x}^{2} - 3x + 1$

a=1[Coefficient of x^2]

b=-3[Coefficient of x]

c=1[Constant term]

NOW, D=${b}^{2} - 4ac$

$D= { - 3}^{2} - 4 \times 1 \times 1 \\ = 9 - 4 \\ = 5$

Now, x=$( - b [plus minus] \sqrt{D} ) \div 2$

Therefore

$x = (3 + \sqrt{5} ) \div 2 \\ x = (3 - \sqrt{5} ) \div 2$