<p class="ql-block ql-indent-1"><span style="font-size:20px;">原来别人早用“韦达定理”偷跑</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">a+b=16，ab=28，多数人列方程、消元、配方，草稿纸翻山越岭。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">同桌瞄一眼，直接写x²-16x+28=0，两根秒出，10秒交卷。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">她没多聪明，只是记得课本角落那句：</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">“</span><b style="font-size:22px;">和与积，就是方程的系数</b><span style="font-size:20px;">。”</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">老师把它当定义，她把它当外挂。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">考试拼的不是算力，是眼力。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">看出出题人埋的暗号，就能跳过迷宫。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">别再把瑞士军刀当螺丝刀用。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">下次看到和与积，先问一句：</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">“韦达定理，能不能直接抄答案？”</span></p><p class="ql-block ql-indent-1"><br></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">已知a + b = 16，则b = 16 - a，将其代入ab = 28可得：</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">a(16 - a) = 28</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">展开式子得到：</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">16a - a^2 = 28</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">移项化为标准的一元二次方程形式：</span></p><p class="ql-block ql-indent-1"><b style="font-size:22px;">a^2 - 16a + 28 = 0</b></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">对于一元二次方程ax^2 + bx + c = 0（这里x=a，a = 1，b = -16，c = 28），求根公式。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">先计算判别式\Delta = b^2 - 4ac = (-16)^2 - 4×1×28 = 256 - 112 = 144。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">则a =。。。。。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">当取+号时a = 14</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">此时b = 16 - 14 = 2。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">当取-号时：</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">a = 2</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">此时b = 16 - 2 = 14。</span></p><p class="ql-block ql-indent-1"><span style="font-size:20px;">综上，a = 2，b = 14或者a = 14，b = 2。</span></p>