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a) Áp dụng hằng đằng thức hiệu của 2 bình phương ta có
\(x^2-7=x^2-\left(\sqrt{7}\right)^2=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)
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Ta có: \(8-27x^6y^3\)
\(=2^3-\left(3x^2y\right)^3\)
\(=\left(2-3x^2\right)\left(4+6x^2y+9x^4y^2\right)\)
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\(x^2-7x+12=x^2-3x-4x+12=x\left(x-3\right)-4\left(x-3\right)=\left(x-3\right)\left(x-4\right)\)
\(x^2-2x-3=x^2+x-3x-3=x\left(x+1\right)-3\left(x+1\right)=\left(x+1\right)\left(x-3\right)\)
\(x^2+3x-18=x^2-3x+6x-18=x\left(x-3\right)+6\left(x-3\right)=\left(x-3\right)\left(x+6\right)\)
a,x2-7x+12=(x-4)(x-3)
b,3x2+13x-10=(3x-2)(x+5)
c,x2-2x-3=(x-3)(x+1)
d,x2+3x-18=(x-3)(x+6)
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1/
a) x2 + 7x + 22 = x2 + 2.(7/2).x + 49/4 - 49/4 + 4 = (x + 7/2)2 + 33/4
ta có (x + 7/2)2 >= 0
=> (x + 7/2)2 +33/4 > 0 (đpcm)
b) x2 + 3x + 4 = x2 + 2.3/2.x + 9/4 - 9/4 + 4 = (x + 3/2)2 + 7/4
ta có (x + 3/2)2 >= 0
=> (x + 3/2)2 + 7/4 > 0 (đpcm)
2/ a) x2 - 3x + 2 = x2 - 2.3/2.x + 9/4 - 9/4 + 2 = (x - 3/2)2 - 1/4 = (x - 3/2 - 1/2)(x - 3/2 + 1/2) = (x - 2)(x - 1)
b) x2 - 6x + 1 = x2 - 2.3.x + 9 - 9 + 1 = (x - 3)2 - 8 = (x - 3 - \(\sqrt{8}\))( x - 3 + \(\sqrt{8}\))
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1) Có 3 = (22 - 1)
=> BT = (22 - 1)(22 + 1)(24 + 1)(28 + 1)(216 +1)
= (24 - 1)(24 + 1)(28 + 1)(216 +1)
= (28 - 1)(28 + 1)(216 +1)
= (216 - 1)(216 +1)
= 232 - 1
\(ta\)\(có\)\(a^5+1=a^5+a^4-a^4-a^3+a^3+a^2-a^2+1\)
\(=a^4\left(a+1\right)-a^3\left(a+1\right)+a^2\left(a+1\right)+\left(-a+1\right)\left(a+1\right)\)
\(=\left(a+1\right)\left(a^4-a^3+a^2-a+1\right)\)