设a,b,c为△ABC的三边长,且二次三项式x²+2ax+b²与x²+2cx-b²有一次公因式,求证△ABC是直角三角形
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![设a,b,c为△ABC的三边长,且二次三项式x²+2ax+b²与x²+2cx-b²有一次公因式,求证△ABC是直角三角形](/uploads/image/z/2832440-32-0.jpg?t=%E8%AE%BEa%2Cb%2Cc%E4%B8%BA%E2%96%B3ABC%E7%9A%84%E4%B8%89%E8%BE%B9%E9%95%BF%2C%E4%B8%94%E4%BA%8C%E6%AC%A1%E4%B8%89%E9%A1%B9%E5%BC%8Fx%26%23178%3B%2B2ax%2Bb%26%23178%3B%E4%B8%8Ex%26%23178%3B%2B2cx-b%26%23178%3B%E6%9C%89%E4%B8%80%E6%AC%A1%E5%85%AC%E5%9B%A0%E5%BC%8F%2C%E6%B1%82%E8%AF%81%E2%96%B3ABC%E6%98%AF%E7%9B%B4%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2)
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