已知方程(2012x)²-2011×2013x-1=0的较大根为m,方程x²+2011x-2012=0的较小根为n,则m-n的值为
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![已知方程(2012x)²-2011×2013x-1=0的较大根为m,方程x²+2011x-2012=0的较小根为n,则m-n的值为](/uploads/image/z/1016526-30-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%96%B9%E7%A8%8B%EF%BC%882012x%EF%BC%89%26%23178%3B-2011%C3%972013x-1%3D0%E7%9A%84%E8%BE%83%E5%A4%A7%E6%A0%B9%E4%B8%BAm%2C%E6%96%B9%E7%A8%8Bx%26%23178%3B%2B2011x-2012%3D0%E7%9A%84%E8%BE%83%E5%B0%8F%E6%A0%B9%E4%B8%BAn%2C%E5%88%99m-n%E7%9A%84%E5%80%BC%E4%B8%BA)
已知方程(2012x)²-2011×2013x-1=0的较大根为m,方程x²+2011x-2012=0的较小根为n,则m-n的值为
已知方程(2012x)²-2011×2013x-1=0的较大根为m,方程x²+2011x-2012=0的较小根为n,则m-n的值为
已知方程(2012x)²-2011×2013x-1=0的较大根为m,方程x²+2011x-2012=0的较小根为n,则m-n的值为
m = { 2011 × 2013 + √[ (2011×2013 )² + 4 × 2012²]} / [2 × (2013 )²]
= {(2012 - 1) × (2012 + 1) + √[ ( × )² + 4 × 2012²]} / [2 × 2012²]
= {(2012² - 1²) + √[ (2012² - 1²)² + 4 × 2012²]} / [2 × 2012²]
= {(2012² - 1) + √[ (2012²)² - 2 × 2012² + (1²)² + 4 × 2012²]} / [2 × 2012²]
= {(2012² - 1) + √[ (2012²)² + 2 × 2012² + (1²)² ]} / [2 × 2012²]
= {(2012² - 1²) + √[ (2012² + 1²)² ]} / [2 × 2012²]
= {(2012² - 1²) + (2012² + 1²) } / [2 × 2012²]
= { 2 × 2012²) } / [2 × 2012²]
= 1
x²+2011x-2012 = (x - 1)(x + 2012) = 0
n = - 2012
m - n = 2013