1/x+x/2=11/6 transformable to quadratic equations

Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).

Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

We are given the algebraic equation:  1/x+x/2=11/6

Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.

LCD(x,2,6) = 6x

Multiply all through the fractions by 6x

(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)

6 + 3x² = 11x

Rewriting the equation:

3x² - 11x + 6 = 0

Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

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Note: Consider we need to find the solution of given equation.

Given:

The equation is

To find:

The solution of the equation.

Solution:

We have,

By cross multiplication, we get

Divide both sides by 2.

Splitting the middle term, we get

Using zero product property, we get

and

and

Therefore, the solutions of the given equation are and .

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step-by-step explanation:

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