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3 years ago

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Solve 9^x-10x3^x+9=0

1 answer:

Goshia [24]3 years ago

4 0

Let y = 3^x , then 9^x = (3^2)^x = (3^x)^2 = y^2, so we can write the equation as

y^2 - 10y + 9 = 0

(y - 9)(y - 1) = 0

giving y = 9 or y = 1

Therefore 3^x = 9 giving x = 2

and 3^x = 1 giving x = 0

so the solution set is {0, 2}

Note - I have assumed that the 'x' after the 10 means 'multiply'. Is that correct?

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The solution to the equations are:

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x² - x + 4 = 0 has no real solutions
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<h3>Part A: Describe the solution</h3>

The equation is given as:

$9x\² - 36x + 36 = 0$

The above equation is a quadratic equation which can be represented as:

$ax\² + bx + c = 0$

The discriminant (d) is calculated as:

$d = b\² - 4ac$

So, we have:

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A discriminant of 0 means that the equation has two equal real solutions

Hence, 9x² - 36x + 36 = 0 has two equal real solutions

<h3>Part B: Describe the solution</h3>

The equation is given as:

$x\² - x + 4 = 0$

The above equation can be represented as:

$ax\² + bx + c = 0$

The discriminant (d) is calculated as:

$d = b\² - 4ac$

So, we have:

$d = (-1)\² - 4 * 1 * 4$

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<h3>Part C: The solution to the expression</h3>

We have:

$4x\² + 23 - 35$

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Read more about quadratic expressions at:

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