Tìm x biết
c) 3x(x – 2) – x^2 + 2x = 0 d) x + 5 = 2(x+5)^2
e) 4x^2 – 25 – (2x – 5)(2x + 7) = 0 f) x^2 + x -12 = 0
Tìm x biết
c) 3x(x – 2) – x^2 + 2x = 0 d) x + 5 = 2(x+5)^2
e) 4x^2 – 25 – (2x – 5)(2x + 7) = 0 f) x^2 + x -12 = 0
Đáp án:
Giải thích các bước giải:
c)3x.(x-2) -x² +2x =0
⇔3x² -6x -x² +2x=0
⇔2x² -4x =0
⇔2x.(x-2) =0
⇔\(\left[ \begin{array}{l}x=0\\x-2=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=0\\x =2\end{array} \right.\)
d)x+5 =2.(x+5)²
⇔(x+5) -2.(x+5)²=0
⇔(x+5).( 1-2.(x+5) =0
⇔(x+5).(1 -2x -10)=0
⇔(x+5).(-2x -9)=0
⇔\(\left[ \begin{array}{l}x+5=0\\-2x-9=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x =-5\\x =-9/2\end{array} \right.\)
e)4x² -25 -(2x -5).(2x+7) =0
⇔4x² -25 -(4x² +4x -35)=0
⇔4x² -25 -4x² -4x +35 =0
⇔-4x +10=0
⇔4x =10
⇔ x=$\frac{5}{2}$
f) x² +x -12=0
⇔x² -4x +3x -12=0
⇔x.(x-4) +3.(x-4)=0
⇔(x-4).(x+3)=0
⇔\(\left[ \begin{array}{l}x-4=0\\x+3=0\end{array} \right.\)
⇔\(\left[ \begin{array}{l}x=4\\x =-3\end{array} \right.\)
Đáp án:
Giải thích các bước giải:
a, 3x(x-2) -x^2 +2x=0
⇔ 3x^2 -6x -x^2 +2x=0
⇔ 2x^2 -4x =0
⇔ 2x(x-2)=0
⇒ x=0 hoặc (x-2)=0 ⇒x=2
d, x+5=2(x+5)^2
⇔ x+5 -2(x+5)^2 =0
⇔ (x+5)[1-2(x+5)]=0
⇔(x+5) (1-2x-10)=0
⇔ (x+5)( -2x-9)=0
⇒ x+5=0 ⇒x=-5
hoặc -2x-9=0 ⇒ x=-9/2
e, 4x^2-25 -(2x-5)(2x-7)=0
⇔(2x-5)(2x+5)-(2x-5)(2x-7)=0
⇔(2x-5)(2x+5-2x+7)=0
⇔(2x-5)12=0
⇒ 2x-5=0. ⇒ x=5/2
f, x^2 +x-12=0
⇔x^2 -3x+4x-12=0
⇔x(x-3)+4(x-3)=0
⇔(x-3)(x+4)=0
⇒x-3=0 ⇒ x=3
hoặc x+4=0 ⇒ x=-4