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Solve For X X+1/X=3, X ≠ 0 - CBSE Class 10 - Mathematics

ConceptRelationship Between Discriminant and Nature of Roots

Question

Solve for x

x+1/x=3, x ≠ 0

Solution

We have been given,

x+1/x=3, x ≠ 0

Now, we solve the equation as follows:

(x^2+1)/x=3

x2 + 1 = 3x

x2 - 3x + 1 = 0

Now we also know that for an equation ax2 + bx + c = 0, the discriminant is given by the following equation:

D = b2 - 4ac

Now, according to the equation given to us, we have,a = 1, b = -3 and c = 1.

Therefore, the discriminant is given as,

D = (-3)2 - 4(1)(1)

= 9 - 4

= 5

Now, the roots of an equation is given by the following equation,

x=(-b+-sqrtD)/(2a)

Therefore, the roots of the equation are given as follows,

x=(-(-3)+-sqrt5)/(2(1))

=(3+-sqrt5)/2

Now we solve both cases for the two values of x. So, we have,

x=(3+sqrt5)/2

Also,

x=(3-sqrt5)/2

Therefore, the value of x=(3+sqrt5)/2, (3-sqrt5)/2

Is there an error in this question or solution?

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Solution Solve For X X+1/X=3, X ≠ 0 Concept: Relationship Between Discriminant and Nature of Roots.
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