Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

Given:

taking LCM

cross multiplying

x^{2} + 1 = 3x

x^{2} – 3x + 1 = 0

Comparing with standard quadratic equation ax^{2} + bx + c = 0

a = 1, b = – 3, c = 1

Discriminant D = b^{2} – 4ac

= (– 3)^{2} – 4.1.1

= 9 – 4 = 5 >

Hence the roots of equation are real.

√D = √5

Roots α and β are given by

Hence the roots of equation are

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