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Question

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

x+1x=3, x0

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Solution

The given equation is

x+1x=3, x0x2+1x=3x2+1=3xx2-3x+1=0

This equation is of the form ax2+bx+c=0, where a = 1, b = −3 and c = 1.

∴ Discriminant, D = b2-4ac=-32-4×1×1=9-4=5>0

So, the given equation has real roots.

Now, D=5

α=-b+D2a=--3+52×1=3+52β=-b-D2a=--3-52×1=3-52

Hence, 3+52 and 3-52 are the roots of the given equation.

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