Đáp án:
Giải thích các bước giải:
$1.$
$a,(4x-1)(16x^2+4x+1)=64x^3-1$
$3.$
$H=x^3-9x^2+27x-27$
$=(x-3)^3$
$⇔(5-3)^3=2^3=8$
$B=8x^3-60x^2+150x-125$
$=(2x-5)^3$
$⇔(2.4-5)^3=3^3=27$
$D=x^3+9x^2+27x+27$
$=(x+3)^3$
$⇔(-103+3)^3=(-100)^3=-1000000$
$4.$
$a,(5-2x)^2-16=0$
$⇔(5-2x-4)(5-2x+4)=0$
⇔\(\left[ \begin{array}{l}1-2x=0\\9-2x=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=\dfrac{9}{2}\end{array} \right.\)
$b,4x^2-3x=7$
$⇔4x^2-3x-7=0$
$⇔4x^2+4x-7x-7=0$
$⇔(4x-7)(x+1)=0$
⇔\(\left[ \begin{array}{l}x=\dfrac{7}{4}\\x=-1\end{array} \right.\)
$e,(x+1)^3-(x-1)^3-6(x-1)^2=-10$
$⇔x^3+3x^2+3x+1-x^3+3x^2-3x+1-6(x^2-2x+1)=-10$
$⇔6x^2-6x^2+12x-6=-10-1-1$
$⇔12x=-12+6$
$⇔12x=-6$
$⇔x=-\dfrac{1}{2}$
