己知:a+b+c=0 求证:①a^3+a^2 c+b^2 c+b^3=abc ②a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2
来源:学生作业帮助网 编辑:作业帮 时间:2024/09/02 06:12:06
![己知:a+b+c=0 求证:①a^3+a^2 c+b^2 c+b^3=abc ②a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2](/uploads/image/z/12529052-44-2.jpg?t=%E5%B7%B1%E7%9F%A5%EF%BC%9Aa%2Bb%2Bc%3D0+%E6%B1%82%E8%AF%81%EF%BC%9A%E2%91%A0a%5E3%2Ba%5E2+c%2Bb%5E2+c%2Bb%5E3%3Dabc+%E2%91%A1a%5E4%2Bb%5E4%2Bc%5E4%3D2a%5E2b%5E2%2B2b%5E2c%5E2%2B2c%5E2a%5E2)
xPJ@Pd&$tQGbTW*(t1bZwo7w{ wՠ{uk&^ۼAu (Ґ^
ˆ @/,_P
W~Ճw0Xnӿ<GM=(nSm* 0lpQ.p~)4{OWGOC~ 2~L8D _T |YM.<k+2%V604Kfn
US6z*Dkf)cK!*bf)F,r}8$wv((˦\قb"v<8b\R?iRb[8BaK"zϰ~$||k8Y
己知:a+b+c=0 求证:①a^3+a^2 c+b^2 c+b^3=abc ②a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2
己知:a+b+c=0 求证:①a^3+a^2 c+b^2 c+b^3=abc ②a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2
己知:a+b+c=0 求证:①a^3+a^2 c+b^2 c+b^3=abc ②a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2
(1)由立方和公式可得
a^3+b^3=(a+b)(a^2-ab+b^2)
因为a+b+c=0.所以a+b=-c
所以a^3+b^3=(-c)(a^2-ab+b^2)=-a^2 c-b^2 c+abc
所以a^3+a^2 c+b^2 c+b^3
=-a^2 c-b^2 c+abc+a^2 c+b^2 c
=abc
(2)
己知:a+b+c=0 求证:①a^3+a^2 c+b^2 c+b^3=abc ②a^4+b^4+c^4=2a^2b^2+2b^2c^2+2c^2a^2
己知:如图,直线a,b被直线C所截,a//b,求证:
己知a,b,c∈R+,a十b十c=|,求证a2十b2十c2≥1/3
己知a、b、c为实数,且a+b+c=1,求证:1/a^2+1/b^2+1/c^2>=27
己知ab不等于零,求证a+b=1的充要条件是a^3+b^3+ab-a^2-b^2=0
己知ab不等于零,求证a+b=1的充要条件是a^3+b^3+ab-a^2-b^2=0
己知4A-B+2C=0,A=B=-2C/3,如何求ABC
己知A=a*a+b*b-c*cB=-4*a*a+2*b*b+3*c*c并且A+B+C=0则C为
己知4A-B+2C=0,A=B=-2C/3,如何求到A=2=B,C=-3
己知直线a∥b,a,b分别与c交于A,B两点,求证;a,b,c三线在同一平面内
己知b>a>0,a ^+b^=4ab,求a+b/a-b
己知|a-2l+lb-3l+lc-4l=0,求式子a+b+c的值
1、当a+b+c=0时,求证:a3+b3+c3=3abc2、①(x+y)(___________)=x4-y4②(x-y)(__________)=x4-y4③(x+y)( ___________)=x5+y5④(x-y)(__________)=x5-y5 3、己知a+b=1, 求证:a3+b3-3ab=14、己知a2=a+1,
A+B=C 己知A+B+C=16.2 A-B=3.3 A=( )
己知实数a、b、c满足1/2|a-b|+根号(2b+c)+(c-1/2)平方=0求a(b+C)的值
己知a,b,c都是质数,且a+b=c,那么a*b*c的最小值是多少
己知a>0,b|b|,则a+b是多少
1、己知三角形ABC的三边a、b、c满足条件a²+b²+c²+338=10a+24b+2bc,试求出a、b、c的值.2、变式题:己知根号(a²+64)+|b³-27|=0,求(a-b)b次方的立方根.3、己知a小于0,b小于0,求4a²+1