当正实数x,y满足等式x+y+8=xy 时 ∴x+y+8≤ (x+y)²/4 ∴(x+y-8)·(x+y+4)≥0请讲解一下x+y+8≤ (x+y)²/4 是怎么化解为(x+y-8)·(x+y+4)≥0的?
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![当正实数x,y满足等式x+y+8=xy 时 ∴x+y+8≤ (x+y)²/4 ∴(x+y-8)·(x+y+4)≥0请讲解一下x+y+8≤ (x+y)²/4 是怎么化解为(x+y-8)·(x+y+4)≥0的?](/uploads/image/z/7663941-45-1.jpg?t=%E5%BD%93%E6%AD%A3%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3%E7%AD%89%E5%BC%8Fx%2By%2B8%3Dxy+%E6%97%B6+%E2%88%B4x%2By%2B8%E2%89%A4+%28x%2By%29%26%23178%3B%2F4+%E2%88%B4%EF%BC%88x%2By-8%EF%BC%89%C2%B7%EF%BC%88x%2By%2B4%EF%BC%89%E2%89%A50%E8%AF%B7%E8%AE%B2%E8%A7%A3%E4%B8%80%E4%B8%8Bx%2By%2B8%E2%89%A4+%28x%2By%29%26%23178%3B%2F4+%E6%98%AF%E6%80%8E%E4%B9%88%E5%8C%96%E8%A7%A3%E4%B8%BA%EF%BC%88x%2By-8%EF%BC%89%C2%B7%EF%BC%88x%2By%2B4%EF%BC%89%E2%89%A50%E7%9A%84%3F)
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当正实数x,y满足等式x+y+8=xy 时 ∴x+y+8≤ (x+y)²/4 ∴(x+y-8)·(x+y+4)≥0请讲解一下x+y+8≤ (x+y)²/4 是怎么化解为(x+y-8)·(x+y+4)≥0的?
当正实数x,y满足等式x+y+8=xy 时 ∴x+y+8≤ (x+y)²/4 ∴(x+y-8)·(x+y+4)≥0
请讲解一下x+y+8≤ (x+y)²/4 是怎么化解为(x+y-8)·(x+y+4)≥0的?
当正实数x,y满足等式x+y+8=xy 时 ∴x+y+8≤ (x+y)²/4 ∴(x+y-8)·(x+y+4)≥0请讲解一下x+y+8≤ (x+y)²/4 是怎么化解为(x+y-8)·(x+y+4)≥0的?
x+y+8≤(x+y)²/4
两边同乘以4
4(x+y)+32≤(x+y)²
左边移到右边
(x+y)²- 4(x+y)-32≥0
令x+y=t
则 t²-4t-32≥0
所以 (t-8)(t+4)≥0
当正实数x,y满足等式x+y+8=xy 时 ∴x+y+8≤ (x+y)²/4 ∴(x+y-8)·(x+y+4)≥0请讲解一下x+y+8≤ (x+y)²/4 是怎么化解为(x+y-8)·(x+y+4)≥0的?
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