A = (x - 1)(x + 2)(x + 3)(x + 6)
= (x2 + 6x - x - 6)(x2 + 3x + 2x + 6)
= (x2 + 5x - 6)(x2 + 5x + 6)
= (x2 + 5x)2 - 62 \(\ge\) -36
Dấu ''='' xảy ra khi x2 + 5x = 0 <=> x(x + 5) = 0 <=> \(\left[{}\begin{matrix}x=0\\x+5=0\end{matrix}\right.\) <=> \(\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
Vậy Min A = -36 khi x = 0 hoặc x = -5
Tìm x :
a ) \(\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6.\)
b ) \(4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
Tìm x, y, z thỏa \(a\left(a-b\right)+b\left(b-c\right)+c\left(c-a\right)\)
Tìm min \(K=a^3+b^3+c^3-3abc +3ab-3c+5\)
Rút gọn:
a) P = \(\frac{bc}{\left(a-b\right)\left(a-c\right)}+\frac{ca}{\left(b-c\right)\left(b-a\right)}+\frac{ab}{\left(c-a\right)\left(c-b\right)}\)
b) Q = \(\frac{\left(x+\frac{1}{x}\right)^6-\left(x^6+\frac{1}{x^6}\right)-2}{\left(x+\frac{1}{x}\right)^3+x+\frac{1}{x^3}}\)
Giúp mik nhé!
Tìm min :
a) \(A=\left|x-7\right|+\left|x+5\right|\)
b) \(B=\left(2x-1\right)^2-3\left|2x-1\right|+2\)
Chứng minh :
a) \(\left(x-1\right)\left(x^2+x+1\right)=x^3-1\)
b) \(\left(x^3+x^2y+xy^2+y^3\right)\left(x-y\right)=x^4-y^4\)
Tim x
a) \(\left(x+3\right)^3-x.\left(3x+1\right)^2+\left(2x+1\right).\left(4x^2-2x+1-3x^2\right)=54\)
b) \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+6.\left(x+1\right)^2+3x^2=-33\)
Tìm max,min:
a) A = \(\left(2x-1\right)\left(x-3\right)\)
b) B = \(\left(1-2x\right)\left(x-3\right)\)
Tìm x
a) \(\left(2x-1\right).\left(2x+1\right)-4x^2=3\)
b) \(5x.\left(x-3\right)^2-5.\left(x-1\right)^3+15.\left(x+2\right).\left(x-2\right)=5\)
a, rut gon A
b, tim x de a<-1
c, tim cac gia tri nguyen cua x de A co gia tri nguyen
cho bthuc B = \(\left(\frac{x^2}{x^3-4x}+\frac{6}{6-3x}+\frac{1}{x-2}\right)chia\left(x-2+\frac{16-x^2}{x+2}\right)\)rut gon B tính b khi /x/ = 1/2tim x de b=2tim x \(\in\) z de b \(\in\) z
