Bài 1
1, phân tích
a, x^3 + 27 c, x^2 + 3xy – 5x – 15y
b, x^2 – 6x + 5 d, X^3 – 2x^2 + 4xy – 2y^2 – y^3
2, tìm x
a, (2 – 3)^2 – (x – 1)^2 = 0
b, x^2 + x – 12 = 0
a) $x^{3}$ + 27 = $x^{3}$ + $3^{3}$ = (x+3)($x^{2}$ – 3x + 9)
b) $x^{2}$ – 6x + 5 = ($x^{2}$ – 2.3.x + 9) – 4 = $(x-3)^{2}$ – $2^{2}$ = (x – 3- 2)(x – 3 + 2) = (x-5)(x-1)
c) $x^{2}$ + 3xy – 5x – 15y = x(x + 3y) – 5(x+3y) = (x-5)(x+3y)
d) $x^{3}$ – $2x^{2}$ + 4xy – $2y^{2}$ – $y^{3}$ = $x^{3}$ – 2($x^{2}$ – 2xy + $y^{2}$) – $y^{3}$
= (x-y)($x^{2}$ + xy + $y^{2}$) – 2($x^{2}$ – 2xy + $y^{2}$) = (x-y)[($x^{2}$ + xy + $y^{2}$ – 2x + 2y)]
A) x^3+27=x^3+3^3
B) X^2-6X+5
=X^2-X-5X-5
=X(X-1)-5(X-1)
=(X-5)(X-1)
C)X^2+3XY-5X-15Y
=X(X+3Y)-5(X+3Y)
=(X-5)(X+3Y)
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