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6) c) x3 - x2 + x = 1
<=> x3 - x2 + x - 1 = 0
<=> (x3 - x2) + (x - 1) = 0
<=> x2 (x - 1) + (x - 1) = 0
<=> (x - 1) (x2 + 1) = 0
=> x - 1 = 0 hoặc x2 + 1 = 0
* x - 1 = 0 => x = 1
* x2 + 1 = 0 => x2 = -1 => x = -1
Vậy x = 1 hoặc x = -1
Bài 5:
a) Đặt \(A=\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=\left(3^{16}-1\right)\left(3^{16}+1\right)\)
\(\Rightarrow8A=3^{32}-1\)
\(\Rightarrow A=\frac{3^{32}-1}{8}\)
b) (7x+6)2 + (5-6x)2 - (10-12x)(7x+6)
=(7x+6)2 + (5-6x)2 - 2(5-6x)(7x+6)
\(=\left(7x+6-5+6x\right)^2\)
\(=\left(13x+1\right)^2\)
\(a.4\left(x+2\right)-7\left(2x-1\right)+9\left(3x-4\right)=30\\ 4x+8-14x+7+27x-36=30\\ 17x+15=66\\ 17x=51\Rightarrow x=3\)
\(b.2\left(5x-8\right)-3\left(4x-5\right)=4\left(3x-4\right)+11\\ =10x-16-12x+15=12x-16+11\\ -2x-1=12x-5\\ \Leftrightarrow-2x-12x=1-5\\ \Leftrightarrow-14x=-4\\ \Leftrightarrow x=\dfrac{7}{2}\)
\(c.4x^2+3\left(2x^2+1\right)=2x\left(5x-7\right)\\ 4x^2+6x^2+3=10x^2-14x\\ 10x^2+3=10x^2-14x\\ \Leftrightarrow3=14x\\\Rightarrow x=\dfrac{3}{14}\)
\(d.x\left(x^2-7\right)=2x\left(\dfrac{1}{2}x^2+6\right)+8\\ x^3-7x=x^3+12x+8\\ \Leftrightarrow-7x=12x+8\\ \Leftrightarrow-7x-12x=8\\ \Leftrightarrow-19x=8\Rightarrow x=-\dfrac{8}{19}\)
b) x8 +7x4+16
= x8+8x4-x4+16
= (x8+8x4+16) - x4
=(x4+4)2-x4
= (x4+4+x2)(x4+4-x2)
c) x5+x-1
= x5 - x4+x3+x4-x3+x2-x2+x-1
= x3(x2-x+1) + x2(x2-x+1) - (x2-x+1)
= (x2-x+1)(x3+x2 -1)
d)x7+x2+1
=x7-x+x2 +x+1
= x (x6-1) + (x2+x+1)
= x(x3-1)(x3+1) + (x2+x+1)
= x(x3+1)(x-1)(x2+x+1)+(x2+x+1)
= (x2+x+1)[x(x3+1)(x-1) +1]
= (x2+x+1)(x5-x4+x2-x+1)
= x (x-1)(x2+x+1)
e) x5+x4+1
= x5+x4+x3 - x3+1
= x3(x2+x+1) - (x-1)(x2+x+1)
= (x2+x+1)(x3-x+1)
f) x8+x+1
= x8-x2+x2+x+1
= x2(x6-1)+(x2+x+1)
= x2(x3-1)(x3+1) +(x2+x+1)
= (x5+x2)(x-1)(x2+x+1) +(x2+x+1)
= (x2+x+1)(x6-x5+x3-x2+1)
x^3 - 7x - 6 = x^3 + x^2 - x^2 - 6x - x - 6 = (x^3 + x^2) - (x^2 + x) - (6x + 6)
= x^2(x + 1) - x(x + 1) - 6(x + 1) = (x + 1)(x^2 - x - 6) = (x + 1)(x^2 - 3x + 2x - 6)
= (x + 1){(x^2 - 3x) + (2x - 6)} = (x + 1){(x(x - 3) + 2(x - 3)}
= (x + 1)(x - 3)(x + 2)
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