Đáp án:
a) $x=\dfrac{15}{2}$
b) $x=-1$
c) $x=\dfrac{-5}{2}$
d) $x=\dfrac{-13}{10}$
e) $x=\dfrac{25}{16}$
Giải thích các bước giải:
a)
$(x+1)^2-5=x^2+11\\⇔x^2+2x+1-5=x^2+1\\⇔2x-4=11\\⇔2x=15\\⇔x=\dfrac{15}{2}$
b)
$3x(2x-3)-3(3+2x^2)\\⇔6x^2-9x-(9+6x^2)=0\\⇔6x^2-9x-9-6x^2=0\\⇔9x=-9\\⇔x=-1$
c)
$\dfrac{x}{2}-\dfrac{2x}{3}+\dfrac{1}{4}=\dfrac{2}{3}\\⇔\dfrac{x}{2}-\dfrac{2x}{3}+\dfrac{1}{4}-\dfrac{2}{3}\\⇔\dfrac{6x-4.2x+3-2.4}{12}=0\\⇔6x-8x+3-8=0\\⇔2x=-5\\⇔x=\dfrac{-5}{2}$
d)
$\dfrac{x-2}{3}-\dfrac{2x-3}{4}=x-1\\⇔\dfrac{x-2}{3}-\dfrac{2x-3}{4}-(x-1)=0\\⇔\dfrac{4(x-2)-3(2x-3)-12(x-1)}{12}=0\\⇔4(x-2)-3(2x-3)-12(x-1)=0\\⇔4x-8-(6x-9)-(12x-12)=0\\⇔4x-8-6x+9-12x+12=0\\⇔14x=13\\⇔x=\dfrac{13}{14}$
e)
$\dfrac{5-2x}{3}+\dfrac{1}{2}=2(x-1)\\⇔\dfrac{5-2x}{3}+\dfrac{1}{2}-2(x-1)=0\\⇔\dfrac{2(5-2x)+3-12(x-1)}{6}=0\\⇔2(5-2x)+3-12(x-1)=0\\⇔10-4x+3-12x+12=0\\⇔16x=25\\⇔x=\dfrac{25}{16}$
