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A= (a+b)2-2ab=S2-2P
B=(a+b)(a2-ab+b2)=S.(S-P)
C= (a2+b2)2-2a2b2=(S-2P)2-2P2
![](https://rs.olm.vn/images/avt/0.png?1311)
a) a^3+b^3
=(a+b).(a^2-ab+b^2)
=S.(a^2+2ab+b^2-3ab)
=S.(a+b)^2-3ab
=S.S^2-3P
=S^3-3P
![](https://rs.olm.vn/images/avt/0.png?1311)
A = a2 + b2
= a2 + 2ab + b2 - 2ab
= ( a + b )2 - 2ab
= S2 - 2P
B = a3 + b3
= a3 + 3a2b + 3ab2 + b3 - 3a2b - 3ab2
= ( a + b )3 - 3ab( a + b )
= S3 - 3PS
= S( S2 - 3P )
C = a4 + b4
= ( a2 )2 + 2a2b2 + ( b2 )2 - 2a2b2
= ( a2 + b2 )2 - 2( a.b )2
=( a2 + 2ab + b2 - 2ab )2 - 2P2
= [ ( a + b )2 - 2ab ]2 - 2P2
= [ S2 - 2P ]2 - 2P2
= S4 - 4PS2 + 4P2 - 2P2
= S4 - 4PS + 2P2
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) a2 + b2 = a2 + b2 + 2ab - 2ab = (a + b)2 - 2ab = s2 - 2p
b) a3 + b3 = (a + b)(a2 - ab + b2) = (a + b)(a2 + 2ab + b2 - 3ab) = (a + b).[(a + b)2 - 3ab] = s.(s2 - 3p) = s3 - 3ps
c) a4 + b4 = a4 + b4 + 4a2b2 - 4a2b2 = (a2 + b2)2 - 4(ab)2 = (s2 - 2p)2 - 4p2
= (s2 - 2p - 2p)(s2 - 2p + 2p) = s2.(s2 - 4p) = s4 - 4ps2
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(a^2+b^2=\left(a+b\right)^2-2ab\)
Thay a+b=s; ab vào đa thức trên ta được:
\(\left(a+b\right)^2-2ab=s^2-2p\)
b, \(a^3+b^3=\left(a+b\right)^3+3a^2b-3ab^2\)
\(=\left(a+b\right)^3-3ab.\left(a+b\right)\)
Thay a+b=s; ab=p Ta được:
\(\left(a+b\right)^3-3ab.\left(a+b\right)=s^3-3sp\)
c, \(a^4+b^4=\left(x^2+y^2\right)^2-2x^2y^2\)
\(=\left(s^2-2p\right)^2-2p^2=s^4-4s^2p+2p^2\)
CHÚC HỌC TỐT!!
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = a2 + b2 = a2 + 2ab + b2 - 2ab = ( a + b )2 - 2ab = 52 - 2.6 = 25 - 12 = 13
B = a3 + b3 = a3 + 3a2b + 3ab2 + b3 - 3a2b - 3ab2 = ( a + b )3 - 3ab( a + b ) = 53 - 3.6.5 = 125 - 90 = 35
C = a4 + b4 = a4 + 2a2b2 + b4 - 2a2b2 = ( a2 + b2 )2 - 2a2b2 = [ ( a + b )2 - 2ab ]2 - 2( ab )2
= ( 52 - 2.6 )2 - 2.62
= ( 25 - 12 )2 - 2.36
= 132 - 72
= 169 - 72 = 97
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:(a2+ab+b2)(a2-ab+b2)-(a4+b4)
= (a2+b2)2-a2b2-a4-b4=a4+2a2b2+b4-a2b2-a4-b4=a2b2
Ta có:(a2+ab+b2)(a2-ab+b2)-(a4+b4)
= (a2+b2)2-a2b2-a4-b4=a4+2a2b2+b4-a2b2-a4-b4=a2b2
đáp số : dễ
\(A=a^2+b^2=\left(a+b\right)^2-2ab=S^2-2P\)
\(B=a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)=S\cdot\left(S^2-3P\right)\)
\(C=a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=\left(S^2-2P\right)^2-2P^2\)