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a: Ta có: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)
\(\Leftrightarrow x^3+8-x^3-2x=15\)
\(\Leftrightarrow2x=-7\)
hay \(x=-\dfrac{7}{2}\)
b: Ta có: \(\left(x-2\right)^3-\left(x-4\right)\left(x^2+4x+16\right)+6\left(x+1\right)^2=49\)
\(\Leftrightarrow x^3-6x^2+12x-8-x^3+64+6\left(x+1\right)^2=49\)
\(\Leftrightarrow-6x^2+12x+56+6x^2+12x+6=49\)
\(\Leftrightarrow24x=-13\)
hay \(x=-\dfrac{13}{24}\)
a) \(x^2+4x+4=\left(x+2\right)^2\)
b) \(\left(x-3\right)\left(x^2+3x+9\right)=x^3-27\)
c) \(x^2-1=\left(x-1\right)\left(x+1\right)\)
d) \(36x^2+36x+9=9\left(2x+1\right)^2\)
Min ra kết quả lun nha bn!
a, (x+2)2
b, x3-33
c, (x-1)(x+1)
d, 9.(2x+1)2
\(a,\Leftrightarrow2x^3-x^2+ax+b=\left(x-1\right)\left(x+1\right)\cdot a\left(x\right)\)
Thay \(x=1\Leftrightarrow2-1+a+b=0\Leftrightarrow a+b=-1\)
Thay \(x=-1\Leftrightarrow-2-1-a+b=0\Leftrightarrow b-a=3\)
Từ đó ta được \(\left\{{}\begin{matrix}a+b=-1\\-a+b=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-2\\b=1\end{matrix}\right.\)
\(b,\Leftrightarrow ax^3+bx^2+2x-1=\left(x-1\right)\left(x+6\right)\cdot b\left(x\right)\)
Thay \(x=1\Leftrightarrow a+b+2-1=0\Leftrightarrow a+b=-1\)
Thay \(x=-6\Leftrightarrow-216a+36b+12-1=0\Leftrightarrow216a-36b=11\)
Từ đó ta được \(\left\{{}\begin{matrix}a+b=-1\\216a-36b=11\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-\dfrac{25}{252}\\b=-\dfrac{227}{252}\end{matrix}\right.\)
\(c,\Leftrightarrow ax^4+bx^3+1=\left(x+1\right)^2\cdot c\left(x\right)\)
Thay \(x=-1\Leftrightarrow a-b+1=0\Leftrightarrow b=a+1\)
\(\Leftrightarrow ax^4+\left(a+1\right)x^3+1⋮\left(x+1\right)\\ \Leftrightarrow ax^4+ax^3+x^3+1⋮\left(x+1\right)\\ \Leftrightarrow ax^3\left(x+1\right)+\left(x+1\right)\left(x^2-x+1\right)⋮\left(x+1\right)\\ \Leftrightarrow\left(x+1\right)\left(ax^3+x^2-x+1\right)⋮\left(x+1\right)\\ \Leftrightarrow ax^3+x^2-x+1⋮\left(x+1\right)\)
Thay \(x=-1\Leftrightarrow-a+1+1+1=0\Leftrightarrow a=3\Leftrightarrow b=4\)
\(a,\left(x+1\right)^3+\left(2-x\right)\left(4+2x+x^2\right)+3x\left(x+2\right)=17\)\(\Leftrightarrow x^3+3x^2+3x+1+8-x^3+3x^2+6x-17=0\)\(\Leftrightarrow6x^2+9x-8=0\)
\(\Leftrightarrow x^2+\dfrac{3}{2}x-\dfrac{4}{3}=0\)
\(\Leftrightarrow\left(x^2+\dfrac{3}{2}x+\dfrac{9}{16}\right)-\dfrac{9}{16}-\dfrac{4}{3}=0\)
\(\Leftrightarrow\left(x+\dfrac{3}{4}\right)^2=\dfrac{91}{48}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{3}{4}=\sqrt{\dfrac{91}{48}}\\x+\dfrac{3}{4}=-\sqrt{\dfrac{91}{48}}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{91}{48}}-\dfrac{3}{4}\\x=-\sqrt{\dfrac{91}{48}}-\dfrac{3}{4}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-9+\sqrt{273}}{12}\\x=-\dfrac{9+\sqrt{273}}{12}\end{matrix}\right.\)
b, \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-2\right)=15\)
\(\Leftrightarrow x^3+8-x^3+2x-15=0\)
\(\Leftrightarrow2x=7\Rightarrow x=\dfrac{7}{2}\)
1)(x^2+3x+1)(x^2+3x+2)-6
Đặt t = x2 + 3x + 1
Khi đó PT có dạng:
t.(t + 1) - 6
= t2 + t - 6
= t2 - 2t - 3t - 6
= t.(t - 2) + 3.(t - 2)
= (t + 3).(t - 2)
= (x2 + 3x + 1 + 3).(x2 + 3x + 1 - 2)
= (x2 + 3x + 4).(x2 + 3x - 1)
\(1\hept{\begin{cases}\left(x^2+3x+2-1\right)\left(x^2+2x+2\right)-6\\\left(t-1\right)\left(t\right)-6\\t^2-t-6\end{cases}}.\) " đặt x^2+3x+2 = t
\(\hept{\begin{cases}t^2-\frac{2t.1}{2}+\frac{1}{4}-\left(\frac{24+1}{4}\right)\\\left(t-\frac{1}{2}\right)^2-\frac{25}{4}\\\left(t-\frac{1}{2}\right)^2-\frac{25}{4}\end{cases}}\)
\(\hept{\begin{cases}\left(t-\frac{1}{2}-\frac{5}{2}\right)\left(t-\frac{1}{2}+\frac{5}{2}\right)\\\left(t-\frac{7}{2}\right)\left(t+\frac{4}{2}\right)\\\left(t-\frac{7}{2}\right)\left(t+\frac{4}{2}\right)\end{cases}}\)
2) \(\hept{\begin{cases}\left\{\left(x+1\right)\left(x+7\right)\right\}\left\{\left(x+5\right)\left(x+3\right)\right\}+15\\\left(x^2+8x+7\right)\left(x^2+8x+15\right)+15\\t\left(t+8\right)+15\end{cases}}\)
\(\hept{\begin{cases}t^2+8t+15\\\left(t^2+8t+16\right)-1\\\left(t+4\right)^2-1\end{cases}}\Leftrightarrow\left(t+5\right)\left(t+4\right)\)
\(\hept{\begin{cases}a^3\left(b-c\right)+b^3\left(c-a+b-b\right)+c^3\left(a-b\right)\\a^3\left(b-c\right)-b^3\left(-c+a-b+b\right)+c^3\left(a-b\right)\\a^3\left(b-c\right)-b^3\left(a-b\right)-b^3\left(b-c\right)+c^3\left(a-b\right)\end{cases}\Leftrightarrow\hept{\begin{cases}\left(b-c\right)\left(a^3-b^3\right)-\left(a-b\right)\left(b^3-c^3\right)\\\left(b-c\right)\left(a-b\right)\left(a^2+ab+b^2\right)-\left(a-b\right)\left(b-c\right)\left(b^2+ab+c^2\right)\\\left(a-b\right)\left(b-c\right)\left(a^2+2ab+2b^2+c^2\right)\end{cases}}}\)
Câu 2:
a) \(A=\left(x+5\right)\left(2x-3\right)-2x\left(x+3\right)-\left(x-15\right)\)
\(=x\left(2x-3\right)+5\left(2x-3\right)-2x^2-6x-x+15\)
\(=2x^2-3x+10x-15-2x^2-6x-x+15\)
\(=0\)
b) \(B=2\left(x-5\right)\left(x+1\right)+\left(x+3\right)-\left(x-15\right)\)
\(=2\left[x\left(x+1\right)-5\left(x+1\right)\right]+x+3-x+15\)
\(=2.\left[\left(x^2+x\right)-\left(5x+5\right)\right]+x+3-x+15\)
\(=2.\left(x^2+x-5x-5\right)+x+3-x+15\)
\(=2x^2+2x-10x-10+x+3-x+15\)
\(=2x^2-8x+8\)
\(=2x\left(x-4\right)+8\)
Thay: \(x=\frac{3}{4}\) vào B ta đc:
\(2.\frac{3}{4}\left(\frac{3}{4}-4\right)+8\)
\(=\frac{3}{2}.\frac{-13}{4}+8\)
\(=\frac{25}{8}\)
c) \(C=5x^2\left(3x-2\right)-\left(4x+7\right)\left(6x^2-x\right)-\left(7x-9x^3\right)\)
\(=5x^23x-5x^22-\left[4x\left(6x^2-x\right)+7\left(6x^2-x\right)\right]-7x+9x^3\)
\(=15x^3-10x^2-\left[4x6x^2-4x^2+42x^2-7x\right]-7x+9x^3\)
\(=15x^3-10x^2-24x^3+4x^2-42x^2+7x-7x+9x^3\)
\(=-48x^2\)
P/s: Ko chắc!
