\(M=2\left(a^3+b^3\right)-3\left(a^2+b^2\right)\)
\(=2\left(a+b\right)\left(a^2+ab+b^2\right)-3a^2-3b^2\)
\(=2a^2+2ab+2b^2-3a^2-3b^2\)
\(=-a^2+2ab-b^2\)
\(=-\left(a^2-2ab+b^2\right)\)
\(=-\left(a-b\right)^2\)
\(=-\left(1-b-b\right)^2=-\left(1-2b\right)^2\)
Cho a+b=1.Tính
M=\(2\left(a^3+b^3\right)-3\left(a^2+b^2\right)\)
cho
\(A=\dfrac{1}{2}+\dfrac{3}{2}+\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3+\left(\dfrac{3}{2}\right)^4+...+\left(\dfrac{3}{2}\right)^{2021}\)
\(B=\left(\dfrac{3}{2}\right)^{2013}:2\)
tính B-A
Tính \(M=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\) biết a+b=1
Cho a+b+c\(a^3+b^3+c^3=3abc\) áp dụng tính B=\(\frac{\left(a^2-b^2\right)^3+\left(b^2-c^2\right)^3+\left(c^2-a^2\right)^3}{\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3}\)
1. Cho a2 - b2 - c2 =3abc
Tính H = \(\left(1-\frac{a}{b}\right)\left(1-\frac{b}{c}\right)\left(1-\frac{c}{a}\right)\)
2. Cho a - b + c = - 4
Tính B = \(\frac{a^3-b^3+c^3+3abc}{\left(a+b\right)^2+\left(b+c\right)^2+\left(c-a\right)^2}\)
Cho a+b=1
Tính \(M=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\)
cho a+b=1
tính \(M=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\)
Cho ab=1 và a+b≠0. Tính
\(P=\frac{1}{\left(a+b\right)^3}\left(\frac{1}{a^3}+\frac{1}{b^3}\right)+\frac{3}{\left(a+b\right)^4}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)+\frac{6}{\left(a+b\right)^5}\left(\frac{1}{a}+\frac{1}{b}\right)\)
a) cho \(a+b+c=2\).tính \(A=\frac{a^3-b^3-c^3-3abc}{\left(a+b\right)^2+\left(b-c\right)^2+\left(a+c\right)^2}\)
b)cho \(a+b+c=0\).tính \(B=\frac{a^2+b^2+c^2}{\left(a-b\right)^2+\left(b-c\right)^2+\left(a-c\right)^2}\)
c) cho \(a+b+c=0;abc\ne0\)tính \(M=\frac{a^3}{b^2+c^2-a^2}+\frac{b^3}{c^2+a^2-b^2}+\frac{c^3}{a^2+b^2-c^2}\)
