Lời giải:
\(17x^2-2x^3-3x^4-4x-5=-3x^4-2x^3+17x^2-4x-5\)
\(=-3x^2(x^2+x-5)+x^3+2x^2-4x-5\)
\(=-3x^2(x^2+x-5)+x(x^2+x-5)+(x^2+x-5)\)
\(=(x^2+x-5)(-3x^2+x+1)\)
Do đó: $(17x^2-2x^3-3x^4-4x-5):(x^2+x-5)=(-3x^2+x+1)$
B1: tính nhẩm
\(101^2\)
\(72^2+56.72+28^2\)
\(45^2\)
\(34.46\)
B2 : Rút gọn
\(A=\left(x+5y\right)^2-5\left(x-2y\right)^2\)
\(B=\left(3x-4\right)^2-2\left(x+11\right)\left(x-11\right)\)
\(C=\left(3x-2y\right)^3-\left(4x-5y\right)\left(16x^2+20xy+25y^2\right)+\left(y+2x\right)^3\)
\(D=\left(x+5\right)\left(x^2-5x+25\right)-\left(x+3\right)^3+\left(x-2\right)\left(x^2+2x+4\right)-\left(x-1\right)^3\)
\(E=-5x\left(x-5\right)+\left(x-3\right)\left(x^2-7\right)\)
Tính
\(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
Giups mk vs nha !! thanks
1)\(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
2)\(4x^2-11x+6=\left(x-1\right)\sqrt{2x^2-6x+6}\)
3)\(9+3\sqrt{x\left(3-2x\right)}=7\sqrt{x}+5\sqrt{3-2x}\)
4)\(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
5)\(\frac{6-2x}{\sqrt{5-x}}+\frac{6+2x}{\sqrt{5+x}}=\frac{8}{3}\)
6)\(2\left(5x-3\right)\sqrt{x+1}+\left(x+1\right)\sqrt{3-x}=3\left(5x+1\right)\)
7)\(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-14x\)
a,\(\frac{3}{x}+\frac{1}{x+3}+\frac{3}{x+6}+\frac{1}{x+7}=\frac{1}{1-x}\)
b, \(\frac{1}{x-5}+\frac{1}{x-2}+\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+3}=\frac{3x-3}{4}\)
c,\(\frac{1}{x-3}+\frac{1}{3x+1}+\frac{10x-13}{4x-6}=\frac{1}{x+1}+\frac{1}{2x-1}+\frac{1}{3x+7}\)
d,\(\frac{x^2+x+1}{2x-1}\left(\frac{3x^2-x+5}{4x-2}-3\right)=8\)
e,\(\frac{2x^2-3}{3x-1}\left(2x-\frac{7+4x}{3x-1}\right)=2\)
f,\(\frac{x\left(3x-1\right)\left(3x^2+1\right)\left(6x^2-3x-1\right)}{\left(x+1\right)^3}=\frac{1}{2}\)
g, \(x\left(x^2+2\right)\left(x^2+2x+8+\frac{12}{x-2}\right)=3\left(x-2\right)\)
help me now
\(\left(x-x^2\right)\left(\sqrt{x-2}+2\right)=2x^3-5x^2+5x-2\)
\(\sqrt{2x-3+\sqrt{4x-7}}+\sqrt{2x+9+5\sqrt{4x-7}}=4\sqrt{2}\)
\(\left(\sqrt{3x+1}-\sqrt{x+2}\right)\left(\sqrt{3x^2+7x+2}+9\right)=6x-3\)
\(\sqrt{5-3x}+\sqrt{x+1}=\sqrt{3x^2-4x+4}\)
\(\Leftrightarrow5-3x+x+1+2\sqrt{\left(5-3x\right)\left(x+1\right)}=3x^2-4x+4\)
\(\Leftrightarrow2\sqrt{-3x^2+2x+5}=3x^2-2x-2\)
\(\Leftrightarrow2\sqrt{-\left(3x^2-2x-5\right)}=3x^2-2x-5+3\)
Đặt \(3x^2-2x-5=t\left(t\le0\right)\)
\(\Rightarrow t=-1\)
\(\Leftrightarrow3x^2-2x-5=-1\)
\(\Leftrightarrow3x^2-2x-4=0\)
\(\Leftrightarrow x=\frac{1+\sqrt{13}}{3}\)
Kiểm duyệt giùm
Phân tích đa thức \(18x^3-\dfrac{8}{25}x\) thành nhân tử
a. \(\dfrac{2}{25}x\left(9x^2-4\right)=\dfrac{2}{25}x\left(3x-2\right)\left(3x+2\right)\)
b. \(2x\left(9x^2-\dfrac{4}{25}\right)=2x\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)\)
Cách phân tích nào đúng, a hay b. Giải thích vì sao?
Cho \(x=\frac{1}{2}\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}\)
Tính \(A=\left(4x^5+4x^4-x^3+1\right)^{19}+\left(\sqrt{x^5+4x^4-5x^3+5x+3}\right)^3+\left(\frac{1-\sqrt{2x}}{\sqrt{2x^2+2x}}\right)\)
Cho \(x=\frac{1}{2}\sqrt{\frac{\sqrt{2}-1}{\sqrt{2}+1}}\) Tính giá trị BT
\(A=\left(4x^5+4x^4-x^3+1\right)^{2018}+\left(\sqrt{4x^5+4x^4-5x^3+3}\right)^3+\left(\frac{1-\sqrt{2}x}{\sqrt{2x^2+2x}}\right)\)tại giá trị x
Giải phương trình:
1: \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^2+2\)
2: \(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{16x-4x^2-15}\)
