What is the positive solution to the equation 0 = -x² + 2x + 1?

Solution:

Given that  –x² + 2x + 1 = 0 

⇒ Multiplying by -1 on both sides, we get x² - 2x - 1 = 0

The quadratic formula is given by x = (-b ± √ (b² - 4ac)) / 2

As we know that coefficient of x²  is a, coefficient of x is b and the constant term is c.

So, a = 1, b = - 2 and c = - 1

Using the quadratic formula, we get,

⇒ x = - (-2) ± √ ((- 2)² - 4 (1) (-1)) / 2 (1) 

⇒ x = - (-2) ± √ (4 + 4) / 2

⇒ x = - (-2) ± √ (8) / 2

On finding the square root, we will have two values of 'x'.

⇒ x = (2 + 2√2) / 2 or x = (2 - 2√2) / 2

⇒ x = 1 + √2 or x = 1 - √2

Hence, we see that 1 + √2 = 1 + 1.414 = 2.414, which is positive and 1 - √2 = 1 - 1.414 = -0.414, which is negative.

Thus, the positive solution to the equation –x² + 2x + 1 = 0 is x = 1 + √2.

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What is the positive solution to the equation 0 = -x² + 2x + 1?

Summary:

The positive solution to the equation 0 = -x² + 2x + 1 is x = 1 + √2.