(一)
解决
x2-7x+2=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X²- 7x + 2 = 0" style="vertical-align:-6px;height:23px;width:106px" loading="lazy">,把答案精确到小数点后两位
“精确到小数点后两位”建议使用二次公式
替代一个= 1,b= -7 andc= 2代入公式,任何负数都用括号括起来
x=--7±-72-4×1×22×1{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X等于分数分子负开括号负7闭括号正负开括号的平方根负7闭括号的平方减去4叉乘1叉乘2终根除以分母2叉乘1终分数" style="vertical-align:-17px;height:52px;width:236px" loading="lazy">
用计算器找出每个解
x= 6.70156…或0.2984…
把最终答案四舍五入到小数点后两位
x= 6.70或x= 0.30
(b)
解决
16x2-82x+45=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="16x²- 82x + 45 = 0" style="vertical-align:-6px;height:23px;width:142px" loading="lazy">
方法1
如果你不能发现因式分解,使用二次公式
替代一个= 16,b= -82 andc= 45代入公式,任何负数都用括号括起来
x=--82±-822-4×16×452×16{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X等于分数分子负开括号负82闭括号正负开括号的平方根负82闭括号的平方减去4叉乘16叉乘45终根除以分母2叉乘16终分数" style="vertical-align:-17px;height:52px;width:272px" loading="lazy">
用计算器找出每个解
x=92{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="粗体9 /粗体2" style="vertical-align:-17px;height:47px;width:19px" loading="lazy">或x=58{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="粗体5 /粗体8" style="vertical-align:-17px;height:47px;width:19px" loading="lazy">
方法2
如果你确实发现了因式分解(2x - 9)(8x - 5),那么就用这种方法代替
2x-98x-5=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="左括号2x - 9右括号8x - 5右括号等于0" style="vertical-align:-6px;height:22px;width:141px" loading="lazy">
将第一个括号设为零
2x-9=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="2 x - 9 = 0" style="vertical-align:-6px;height:22px;width:72px" loading="lazy">
两边都加9,然后除以2
2x=9x=92{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="表中行单元格2 ×端单元格= 9行x = 9除以2 ×端单元格结束表" style="vertical-align:-37px;height:73px;width:54px" loading="lazy">
将第二个括号设为0
8x-5=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="8x - 5 = 0" style="vertical-align:-6px;height:22px;width:72px" loading="lazy">
两边都加5,然后除以8
8x=5x=58{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="表中行单元格8 ×端单元格等于5行x等于单元格5 / 8端单元格结束表" style="vertical-align:-37px;height:73px;width:54px" loading="lazy">
x=92{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="粗体9 /粗体2" style="vertical-align:-17px;height:47px;width:19px" loading="lazy">或x=58{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="粗体5 /粗体8" style="vertical-align:-17px;height:47px;width:19px" loading="lazy">
(c)
通过编写
x2+6x+5{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X²+ 6x + 5" style="vertical-align:-6px;height:23px;width:80px" loading="lazy">在表格中
x+p2+q{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="开括号x + p闭括号²+ q" style="vertical-align:-6px;height:23px;width:84px" loading="lazy">,解决
x2+6x+5=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X²+ 6x + 5 = 0" style="vertical-align:-6px;height:23px;width:106px" loading="lazy">
这道题要求你先完成方框
找到p(中间数字减半)
p=62=3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="P = 6 / 2 = 3" style="vertical-align:-17px;height:47px;width:71px" loading="lazy">
写x2+ 6x(x+p)2-p2
x2+6x=x+32-32=x+32-9{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="表行单元格x的平方加上6x端单元格等于单元格开括号x加3闭括号的平方减去3的平方端单元格行空白等于单元格开括号x加3闭括号的平方减去9端单元格结束表" style="vertical-align:-26px;height:50px;width:159px" loading="lazy">
取代x2+ 6x(x+ 3)2- 9在方程中
x+32-9+5=0x+32-4=0{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="表中行单元格的开括号x加3个闭括号的平方减去9加5个结束单元格等于0行单元格的开括号x加3个结束括号的平方减去4个结束单元格等于0结束表" style="vertical-align:-26px;height:50px;width:134px" loading="lazy">
使x方程的主体(从两边同时加4开始)
x+32=4{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="左括号x + 3右括号的平方等于4" style="vertical-align:-6px;height:23px;width:82px" loading="lazy">
两边同时开根号(加上±号可以得到两个解)
x+3=±4=±2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X + 3 =正负根号4 =正负2" style="vertical-align:-6px;height:26px;width:139px" loading="lazy">
两边同时减去3
x=±2-3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" alt="X等于正负2 - 3" style="vertical-align:-6px;height:22px;width:79px" loading="lazy">
先用+,再用-分别找出每个解
x= - 5,x= - 1
即使二次因式分解为(x+ 5) (x+ 1),这不是问题中要求的方法