phan tích nhan tử thanh nhan tử:
a)\(3x^2-12y^2\)
b)\(5xy^2-10xyt+5xt^2\)
c)\(x^3+3x^2+3x+1-27x^3\)
d)\(\text{a}^3x-\text{a}b+b-x\)
e)\(3x^2\left(\text{a}+b+c\right)+36xy\left(\text{a}+b+c\right)+108y^2\left(\text{a}+b+c\right)\)
f)\(\text{a}b\left(\text{a}-b\right)+bc\left(b-c\right)+c\text{a}\left(c-\text{a}\right)\)
g)\(\left(\text{a}+b+c\right)^3-\text{a}^3-b^3-c^3\)
h)\(4\text{a}^2b^2-\left(\text{a}^2+b^2-c^2\right)^2\)
Cho các số thực không âm a,b,ca,b,c thoả mãn a+b+c=1a+b+c=1. Chứng minh rằng :
\(\sqrt{a+\frac{\left(b-c\right)^2}{4}}+\sqrt{b+\frac{\left(c-a\right)^2}{4}}+\sqrt{c+\frac{\left(a-b\right)^2}{4}}\le\sqrt{3}+\left(1-\frac{\sqrt{3}}{2}\right)\left(\text{|
}a-b\text{|
}\right)+\text{|
}b-c\text{|
}+\text{|
}c-a\text{|
}.\)
phan tích da thuc thanh nhan tu
\(\text{a}b\left(\text{a}-b\right)+bc\left(b-c\right)+c\text{a}\left(c-\text{a}\right)\)
Xác định a,b,c,d thỏa mãn đẳng thức.
a) \(\left(\text{ax+b}\right)\left(x^2+c\text{x+1}\right)=x^3-3\text{x}+2\)
b) \(x^4+\text{ax}^2+b=\left(x^3-3\text{x}+2\right)\left(x^2+c\text{x}+d\right)\)
Mọi người giúp mình nha!
Mạnh mẽ hơn Nesbitt?
Với a, b, c là các số thực sao cho: \(a+b+c>0,\text{ }ab+bc+ca>0,\text{ }\left(a+b\right)\left(b+c\right)\left(c+a\right)>0\) thì:
\(\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}-\frac{3}{2}\ge\left(\Sigma ab\right)\left(\Sigma\frac{1}{\left(a+b\right)^2}\right)-\frac{9}{4}\)
Chứng minh: \(4\left(a+b+c\right)\left(a+b\right)^2\left(b+c\right)^2\left(c+a\right)^2\cdot\left(\text{VT}-\text{VP}\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(c+a\right)\left[\Sigma\left(ab+bc-2ca\right)^2+\left(ab+bc+ca\right)\Sigma\left(a-b\right)^2\right]\)
\(+\left(a+b+c\right)\left(a-b\right)^2\left(b-c\right)^2\left(c-a\right)^2\ge0\)
Rút gọn C=\(\dfrac{\text{ a^2b+b^2c+c^2a-ab^2-bc^2-ca^2}}{a^3\left(b^2-c^2\right)+b^3\left(c^2-a^2\right)+c^3\left(a^2-b^2\right)}\)
phan tich đa thức thanh nhan tử
\(4\text{a}^2b^2-\left(\text{a}^2+b^2-c^2\right)^2\)
Tìm x, biết:
a) \(x\left(x-1\right)-x^2+2\text{x}=5\)
b) \(8\left(x-2\right)-2\left(3\text{x}-4\right)=2\)
c) \(\left(3\text{x}+2\right)\left(x-1\right)-3\left(x+1\right)\left(x-2\right)=4\)
d) \(\left(3\text{x}-5\right)\left(7-5\text{x}\right)-\left(5\text{x}+2\right)\left(2-3\text{x}\right)=4\)
a) Cho \(x+y=2;x^2+y^2=10.\text{tính }x^{3+}y^3\)
b) Cho \(a+b+c=0;a^2+b^2+c^2=2.\text{Tính}:a^4+b^4+c^4\)
c) Cho \(a+b+1=2.\text{Tính}:A=a^3+b^3+3ab\left(a^2+b^2\right)+6a^2b^2\left(a+b\right)\)
Tìm a,b,c sao cho f(x) = g(x) biết:
\(f\left(x\right)=3x^k\left(\text{a.x}^2+bx+c\right)\)
\(g\left(x\right)=3x^{k+2}-12x^k+3^k\)
