已知实数a、b满足(a+b)²=1,(a-b)²=25.求a²+b²+ab的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/06 05:46:52
![已知实数a、b满足(a+b)²=1,(a-b)²=25.求a²+b²+ab的值](/uploads/image/z/3844118-38-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0a%E3%80%81b%E6%BB%A1%E8%B6%B3%28a%2Bb%29%26%23178%3B%3D1%2C%28a-b%29%26%23178%3B%3D25.%E6%B1%82a%26%23178%3B%2Bb%26%23178%3B%2Bab%E7%9A%84%E5%80%BC)
x){}Kl
Iv/|mFvF.gdlcS"jyڰ&HfƥHu@|4 $M]tQ](6$wtt-tȎr
u5t4mm젡b`45z
$'i'G,|g;q@@lr4ueAa4 C$)($eMmX]d.®G$%`.ŕLAU7I I
已知实数a、b满足(a+b)²=1,(a-b)²=25.求a²+b²+ab的值
已知实数a、b满足(a+b)²=1,(a-b)²=25.求a²+b²+ab的值
已知实数a、b满足(a+b)²=1,(a-b)²=25.求a²+b²+ab的值
(a+b)²-(a-b)²=-24
即(a²+b²+2ab)-(a²+b²-2ab)=-24
即4ab=-24
得ab=-6
a²+b²+ab=a²+b²+2ab-ab=(a+b)²-ab=1-(-6)=7
7
1-2式:4ab=-24 ab=-6
a2+b2=25-12=13
答案7
(a+b)²=a^2+b^2+2ab=1
(a-b)²=a^2+b^2-2ab=25
可得a^2+b^2=13 2ab=-12
故a²+b²+ab=7
为7
(a+b)²=a²+b²+2ab=1,(a-b)²=a²+b²-2ab=25
(a+b)²-(a-b)²=4ab=1-25
ab=-6
a²+b²+ab=(a+b)²-ab=1-(-6)=7
a+b)²-(a-b)²=-24
即(a²+b²+2ab)-(a²+b²-2ab)=-24
即4ab=-24
得ab=-6
a²+b²+ab=a²+b²+2ab-ab=(a+b)²-ab=1-(-6)=7