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What is the value of x in the equation (4sqrtx = x² - 9x + 12)?

User Dubbaluga
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Final answer:

The equation 4sqrt(x) = x² - 9x + 12 must be re-arranged and then solved using advanced algebraic techniques such as substitution, turning it into a quadratic equation, which can then be factored or solved using the quadratic formula.

Step-by-step explanation:

To solve the equation 4sqrt(x) = x² - 9x + 12, we first need to isolate the square root term by moving all other terms to the opposite side:

x² - 9x + 12 - 4sqrt(x) = 0

This is not a standard quadratic equation because of the square root present; however, it resembles a quadratic in form. We can attempt to factor it, but this unconventional equation may require more advanced techniques such as substitution.

If we tried substitution, let us say y = sqrt(x), then the equation becomes:

y² - 9y + 12 - 4y = 0

Now, it looks like a quadratic equation in terms of y:

y² - 13y + 12 = 0

Which we can factor or use the quadratic formula to solve for y. Once we have the value(s) of y, we can then square it to find the desired x.

User Oceanexplorer
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