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Đặt biểu thức đã cho là A.
Ta có: 2A = (3 - 1) * (3 + 1) * (3^2 + 1) * .... * (3^64 + 1)
= (3^2 - 1) * (3^2 + 1) * ... * (3^64 + 1) (hằng đẳng thức a^2 - b^ 2 = (a+b)(a-b))
Rút gọn triệt tiêu ta được 2A=3^64 - 1
=> A = (3^64 - 1)/2
\(A=\left(\frac{21}{x^2-9}-\frac{x-4}{3-x}-\frac{x-1}{3+x}\right)\div\left(1-\frac{1}{x+3}\right)\)
\(=\left(\frac{21}{\left(x-3\right)\left(x+3\right)}+\frac{\left(x-4\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\right)\div\left(\frac{x+3}{x+3}-\frac{1}{x+3}\right)\)
\(=\left(\frac{21}{\left(x-3\right)\left(x+3\right)}+\frac{x^2-x-12}{\left(x-3\right)\left(x+3\right)}-\frac{x^2-4x+3}{\left(x-3\right)\left(x+3\right)}\right)\div\frac{x+2}{x+3}\)
\(=\frac{21+x^2-x-12-x^2+4x-3}{\left(x-3\right)\left(x+3\right)}\times\frac{x+3}{x+2}\)
\(=\frac{3x+6}{x-3}\times\frac{1}{x+2}=\frac{3\left(x+2\right)}{\left(x-3\right)\left(x+2\right)}=\frac{3}{x-3}\)
\(A=\left(\frac{21}{x^2-9}-\frac{x-4}{3-x}-\frac{x-1}{3+x}\right):\left(1-\frac{1}{x+3}\right)\)
\(=\left(\frac{21}{x^2-9}+\frac{x-4}{x-3}-\frac{x-1}{x+3}\right):\left(\frac{x+2}{x+3}\right)\)
\(=\left(\frac{21}{\left(x-3\right)\left(x+3\right)}+\frac{\left(x-4\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x-1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}\right):\left(\frac{x+2}{x+3}\right)\)
\(=\left(\frac{21+x^2-x-12-x^2+4x-3}{\left(x-3\right)\left(x+3\right)}\right):\left(\frac{x+2}{x+3}\right)\)
\(=\frac{6+3x}{\left(x-3\right)\left(x+3\right)}.\frac{x+3}{x+2}=\frac{3\left(x+2\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)\left(x+2\right)}=\frac{3}{x-3}\)
\(A=x^3-8-\left(x^3+3x^2+3x+1\right)+3\left(x^2-1\right)\)
\(=x^3-8-x^3-3x^2-3x-1+3x^2-3\)
\(=\left(x^3-x^3\right)+\left(-3x^2+3x^2\right)-3x-8-3\)
\(=-3x-11\)
à bài này dễ mà
đầu tiên nhá:không biết,tiếp theo:ko biết.Thế thôi còn lại bạn tự giải
bạn sử dụng hằng đẳng thức nhé .Mình bít nhg lười viết nắm
a, \(A=\left(-5x+4\right)\left(3x-2\right)+\left(-2x+3\right)\left(x-2\right)\)
\(=-15x^2+10x+12x-8=-15x^2+22x-8\)
Thay x = -2 vào biểu thức ta có : \(-15\left(-2\right)^2+22\left(-2\right)-8\)
\(=-15.4-44-8=-112\)
b, \(B=\left(x-9\right)\left(2x+3\right)-2\left(x+7\right)\left(x-5\right)\)
\(=2x^2+3x-18x-27=2x^2-15x-27\)
Thay x = -1/2 vào biểu thức ta có : \(2\left(-\frac{1}{2}\right)^2-15\left(-\frac{1}{2}\right)-27\)
\(=2.\frac{1}{4}+\frac{15}{2}-27=\frac{11}{2}+\frac{15}{2}+27=40\)
Bài làm:
a) \(A=\left(-5x+4\right)\left(3x-2\right)+\left(-2x+3\right)\left(x-2\right)\)
\(A=-15x^2+22x-8-2x^2+7x-6\)
\(A=-17x^2+29x-14\)
Thay x = -2 vào ta được:
\(A=-17.\left(-2\right)^2+29.\left(-2\right)-14\)
\(A=-68-58-14\)
\(A=-140\)
b) \(B=\left(x-9\right)\left(2x+3\right)-2\left(x+7\right)\left(x-5\right)\)
\(B=2x^2-15x-27-2\left(x^2+2x-35\right)\)
\(B=2x^2-15x-27-2x^2-4x+70\)
\(B=-19x+43\)
Thay x = -1/2 vào B ta được:
\(B=-19.\left(-\frac{1}{2}\right)+43=\frac{19}{2}+43=\frac{105}{2}\)
\(B=\left(3-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=\left(3+1\right)\left(3-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=\left(3^{16}-1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=\left(3^{32}-1\right)\left(3^{32}+1\right)\)
\(\left(3+1\right)B=3^{64}-1\)
\(B=\frac{3^{64}-1}{4}\)
Chúc bạn làm bài tốt
