子路
Lv 6
子路 asked in 科學及數學數學 · 1 decade ago

AL rationality 1

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2 Answers

Rating
  • 1 decade ago
    Favorite Answer

    y = √3 - √2

    y + √2 = √3

    y^2 + 2 + 2y√2 = 3

    √2 = (1 - y^2)/2y

    If y = √3 - √2 is rational , that means (1 - y^2)/2y is rational ,then √2 is

    rational. But we know √2 is not rational . It is impossible.

    So √3 - √2 is not rational.

  • 天助
    Lv 7
    1 decade ago

    if √3-√2 is rational, then 1/(√3-√2)=√3+√2 is rational

    so,[(√3+√2)-(√3-√2)]/2=√2 is rational(contradition)

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