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9 October, 11:13

What is the positive solution to the equation 0 = - x2 + 2x + 1? Quadratic formula: x = StartFraction negative b plus or minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction

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  1. 9 October, 11:29
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    x = 2 + √2

    x = 2 - √2

    Step-by-step explanation:

    - x² + 2x + 1 = 0

    x² - 2x - 1 = 0

    Here,

    a = 1

    b = - 2

    c = - 1

    Now,

    Discriminant

    D = b² - 4ac

    = (-2) ² - 4 (1) (-1)

    = 4 + 4

    = 8

    =2√2 > 0

    Real and Distinct roots

    x = - b + - √b² - 4ac/2a

    = - (-2) + - √ = (-2) ² - 4 (1) (-1) / 2 (1)

    = 2 + - √4 + 4/2

    = 2 + - √8/2

    = 2 + - 2√2/2

    = 2 + - √2

    x = 2 + √2 or x = 2 - √2
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