Đáp án:
Giải thích các bước giải
a, ( x² - 3x - 1)² - 12 ( x² - 3x - 1) + 27
Đặt x² -3x -1 = y
=> y² - 12y + 27 = y² - 2.y.6 + 6² - 9
= (y-6)² - 3² = ( y-6 - 3)(y-6 + 3) = ( y - 9)(y - 3)
= ( x² - 3x -1 - 9)(x² - 3x - 1-3) = (x² - 3x - 10)(x² - 3x - 4)
= (x² - 3x - 10)( x² + x - 4x - 4)
= ( x² - 3x - 10) [x(x+1) - 4( x+1)]
= ( x² - 3x - 10)(x+1)(x-4)
b. ( x+2)(x+3)(x+4)(x+5) - 24 = [(x+2)(x+5)][(x+3)(x+4)] - 24
= (x² + 7x + 10)(x² + 7x + 12) - 24
Đặt x² + 7x + 10 = y
=> y ( y+2) - 24 = y² + 2y - 24 = y² +2y + 1 -25 = (y+1)² - 5²
= ( y+1 - 5)(y+1+5)
= ( y-4)(y+6)
= (x² + 7x + 10 - 4)(x²+ 7x+10+6) = ( x² + 7x + 6) (x²+ 7x + 16)
= (x² + x + 6x + 6)(x² + 7x + 16)
= [x(x+1)+ 6(x+1)](x² + 7x +16)
= (x+1)(x+6)(x² + 7x + 16)
c, ( x² + x) + 4x² + 4x - 12
=> (x² + x) + 4 ( x² + x) = 12
Đặt x² +x = y
=> y + 4y = 12
= 5y = 12
=> y = $\frac{12}{5}$
d, (x²+x+1)(x²+x+2) - 12
Đặt x² + x+ 1 = y
=> y ( y+1) -12 = y² + y -12
