已知a,b为实数,且满足16a²+2a+8ab+b²-1=0,求3a+b的最小值
人气:478 ℃ 时间:2020-03-22 14:36:24
解答
设:3a+b=t,则:b=t-3a代入,得:16a²+2a+8a(t-3a)+(t-3a)²-1=0a²+(2+2t)a+(t²-1)=0因为这个方程中a是实数,则这个方程的判别式:△=(2+2t)²-4(t²-1)≥0得:t≥-1即:t...16a²+2a+8a(t-3a)+(t-3a)²-1=0到a²+(2+2t)a+(t²-1)=0是怎么分解的?这个是关于a的一元二次方程,这个方程一定有解,则判别式大于等于0
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