\(C=x\left(x-3\right)\left(x+3\right)-\left(x+1\right)\left(x^2-7x\right)\)

\(=x\left(x^2-9\right)-x\left(x+1\right)\left(x-7\right)\)

\(=x^3-9x-x^3+7x^2-x^2+7x=6x^2-2x\)

\(=2x\left(3x-1\right)\)Thay x = 2/3 vào biểu thức trên ta được : 

\(2.\frac{2}{3}\left(3.\frac{2}{3}-1\right)=\frac{4}{3}\left(2-1\right)=\frac{4}{3}\)

Ta có:\(C=x\left(x-3\right)\left(x+3\right)-\left(x+1\right)\left(x^2-7x\right)\)

\(=x\left(x^2-9\right)-\left[x\left(x^2-7x\right)+1\left(x^2-7x\right)\right]\)

\(=x^3-9x-x^3+7x^2-x^2+7x\)

\(=-x^2-2x+7\)

\(=6x^2-2x\)

\(=2x\left(3x-1\right)\)

Tại \(x=\frac{2}{3}\)thì giá trị của C là:

\(C=2.\frac{2}{3}\left(3.\frac{2}{3}-1\right)\)

\(=\frac{4}{3}\left(2-1\right)=\frac{4}{3}\)

\(C=x\left(x-3\right)\left(x+3\right)-\left(x+1\right)\left(x^2-7x\right)\)

\(=x\left(x^2-9\right)-\left(x^3-6x^2-7x\right)\)

\(=x^3-9x-x^2+6x^2+7x\)

\(=6x^2+2x\)

\(=2x\left(3x+1\right)\)

với \(x=\frac{2}{3}\)phương trình C trở thành :

\(C=2.\frac{2}{3}.\left(3.\frac{2}{3}+1\right)=2.\frac{2}{3}.3=4\)

Vậy C = 4 với \(x=\frac{2}{3}\)

(4x² - 4x + 1) - (x + 1)² 

 =(2x - 1)² - (x + 1)² 

 = (2x - 1 + x + 1)(2x - 1 - x - 1) 

= 3x(x - 2) 

\(\left(4x^2-4x+1\right)-\left(x+1\right)^2\)

\(=\left(2x-1\right)^2-\left(x+1\right)^2\)

\(=\left(2x-1-x-1\right)\left(2x-1+x+1\right)\)

\(=\left(x-2\right)3x\)

\(VT\ge0\Rightarrow VP\ge0\Rightarrow x^3-1\ge0\Leftrightarrow x\ge1\)

Với \(x\ge1\)thì \(\left|x+1\right|=x+1,\left|x^2+x-2\right|=x^2+x-2\)

Phương trình ban đầu tương đương với:

\(x+1+x^2+x-2=x^3-1\)

\(\Leftrightarrow x^3-x^2-2x=0\)

\(\Leftrightarrow x\left(x-2\right)\left(x+1\right)=0\)

\(\Leftrightarrow x=2\)(vì \(x\ge1\))

a, \(\left(x-15\right)\left(x+15\right)-\left(x+2\right)^2-\left(x-5\right)^2\)

\(=x^2-225-x^2-4x-4-x^2+10x-25\)

\(=-x^2+6x-254\)

b, \(\left(2x-1\right)\left(2x+1\right)+\left(x+9\right)^2-\left(x-3\right)^2\)

\(=4x^2-1+x^2+18x+81-x^2+6x-9=4x^2+24x+71\)

c, \(\left(7x-3\right)^2-\left(x-5\right)\left(x+5\right)-\left(2x+4\right)^2\)

\(=49x^2-42x+9-x^2+25-4x^2-16x-16=44x^2-58x+18\)

 Nếu bn ko nhìn rõ thì ib vs mk nhé, mk sẽ gửi bản full cho bn.

Đấy nhé

\(\left(a+b\right)^3=a^3+b^3+3ab\left(a+b\right)\)

\(\Leftrightarrow2^3=2+3.2.ab\)

\(\Leftrightarrow ab=1\)

\(a^2+b^2=\left(a+b\right)^2-2ab=2^2-2.1=2\)

\(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=2^2-2.1=2\)