Mình xin gửi tặng 20 điểm nha! Giúp mình bài này với ạ! Bạn nào có câu trả lời chính xác + đầu đủ, mình tặng 5 sao + ctlhn cho bạn đó nhé! Tks
Bài 1: Tìm x, biết:
a) 4x^2 – 28x + 49 = 25
b) (3x + 1)^2 – (x – 2)^2 = 0
c) x^2 – 2x = 24
d) x^2- 4 = 8.(x-2)
e) 4x^2 – 12x + 9 = (5-x)^2
(Lưu ý: Bạn nào biết chính xác thì trl nhé! Mấy bạn không biết vui lòng next ạ!)
Đáp án:
Giải thích các bước giải
a, 4x² – 28x + 49 = 25
⇔ (2x)² – 2.2.7x + 7² = 5²
⇔ (2x – 7)² = 5²
⇔ (2x – 7)² – 5² = 0
⇔(2x – 7 – 5).(2x – 7 + 5)=0
⇔ (2x – 12).(2x – 2) = 0
⇔ [2x−12=02x−2=0[2x−12=02x−2=0
⇔ [x=6x=1[x=6x=1
b, (3x + 1)² – (x – 2)² = 0
⇔ [3x + 1 – (x – 2)].(3x + 1 + x – 2) = 0
⇔ (3x + 1 – x + 2).(4x – 1) =0
⇔ (2x + 3).(4x – 1) = 0
⇔ [2x+3=04x−1=0[2x+3=04x−1=0
⇔ [x=−32x=14[x=−32x=14
c, x² – 2x = 24
⇔ x² – 2x + 1 = 25
⇔ (x – 1)² – 5² = 0
⇔ (x – 1 – 5).(x – 1 + 5) = 0
⇔ (x – 6).(x + 4) = 0
⇔ [x−6=0x+4=0[x−6=0x+4=0
⇔ [x=6x=−4[x=6x=−4
d, x² – 4 = 8(x – 2)
⇔ x² – 4 = 8x – 16
⇔ x² – 8x + 16 = 4
⇔ (x – 4)² = 2²
⇔ (x – 4)² – 2² = 0
⇔ (x – 4 – 2).(x – 4 + 2 ) = 0
⇔ (x – 6).(x – 2) = 0
⇔ [x=6x=2[x=6x=2
e, 4x² – 12x + 9 = (5 – x )²
⇔ (2x)² – 2.2x.3 + 3² = ( 5 – x )²
⇔ (2x – 3)² – ( 5 – x)² = 0
⇔ (2x – 3 – 5 + x).(2x – 3 + 5 – x) =0
⇔ (3x – 8).(x +2 ) =0
⇔[x=83x=−2[x=83x=−2
Đáp án:
a, 4x² – 28x + 49 = 25
⇔ (2x)² – 2.2.7x + 7² = 5²
⇔ (2x – 7)² = 5²
⇔ (2x – 7)² – 5² = 0
⇔(2x – 7 – 5).(2x – 7 + 5)=0
⇔ (2x – 12).(2x – 2) = 0
⇔ \(\left[ \begin{array}{l}2x-12=0\\2x-2=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=6\\x=1\end{array} \right.\)
b, (3x + 1)² – (x – 2)² = 0
⇔ [3x + 1 – (x – 2)].(3x + 1 + x – 2) = 0
⇔ (3x + 1 – x + 2).(4x – 1) =0
⇔ (2x + 3).(4x – 1) = 0
⇔ \(\left[ \begin{array}{l}2x+3=0\\4x -1=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\frac{-3}{2} \\x=\frac{1}{4} \end{array} \right.\)
c, x² – 2x = 24
⇔ x² – 2x + 1 = 25
⇔ (x – 1)² – 5² = 0
⇔ (x – 1 – 5).(x – 1 + 5) = 0
⇔ (x – 6).(x + 4) = 0
⇔ \(\left[ \begin{array}{l}x-6=0\\x+4=0\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=6\\x=-4\end{array} \right.\)
d, x² – 4 = 8(x – 2)
⇔ x² – 4 = 8x – 16
⇔ x² – 8x + 16 = 4
⇔ (x – 4)² = 2²
⇔ (x – 4)² – 2² = 0
⇔ (x – 4 – 2).(x – 4 + 2 ) = 0
⇔ (x – 6).(x – 2) = 0
⇔ \(\left[ \begin{array}{l}x=6\\x=2\end{array} \right.\)
e, 4x² – 12x + 9 = (5 – x )²
⇔ (2x)² – 2.2x.3 + 3² = ( 5 – x )²
⇔ (2x – 3)² – ( 5 – x)² = 0
⇔ (2x – 3 – 5 + x).(2x – 3 + 5 – x) =0
⇔ (3x – 8).(x +2 ) =0
⇔\(\left[ \begin{array}{l}x=\frac{8}{3} \\x=-2\end{array} \right.\)