a) (3x – 5)2 – (x +1 )2 = (3x – 5 – x – 1)(3x – 5 + x + 1)
= (2x – 6)(4x – 4) = 8(x – 1)(x – 3)
Vậy (x – 1)(x – 3) = 0 ⇒ x - 1 = 0 hoặc x - 3 = 0
⇒ x = 1hoặc x = 3
b)(5x – 4)2 – 49x2 = (5x – 4)2 – (7x)2 = (5x – 4 – 7x)(5x – 4 + 7x)
= (12x – 4)(-2x – 4) = -8(3x – 1)(x + 2)
Vậy (3x – 1)(x + 2) = 0 ⇒ 3x - 1 = 0 hoặc x + 2 = 0
⇒ x = 1/3 hoặc x = -2
(3x-5)2-(x+1)2=0
<=> (3x-5-x-1)2=0
=>3x-5-x-1=0
<=> 2x-6=0
<=>2x=6
=>x=3 Vậy x=3
a)(3x - 5)2 - ( x+1)2 =0
<=> 6x - 10 - 2x + 2 = 0
<=> 4x = 8 <=> x = 2
Vậy nghiệm của phương trình là x=2
b (5x - 4)2 - 49x2= 0
<=> 10x - 8 - 98 = 0
<=> 10x = 106 <=> x= 10.6
Vậy nghiệm của phương trình là x= 10.6
Ta có :
a) (3x - 5)2 - (x + 1)2 = 0
=> [(3x - 5) - (x + 1)].[(3x - 5) + (x + 1)] = 0
=> (2x - 6).(4x - 4) = 0
=> 2(x - 3).2(x - 2) = 0
=> (x - 3)(x - 2) = 0
=> \(\orbr{\begin{cases}x-3=0\\x-2=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=3\\x=2\end{cases}}\)
Vậy ...
b) Ta có : (5x - 4)2 - 49x2 = 0
=> (5x - 4 + 7x)(5x - 4 - 7x) = 0
=> (12x - 4)(-2x - 4) = 0
=> 4(3x - 1). (-2).(x + 2) = 0
=> (3x - 1)(x + 2) = 0
=> \(\orbr{\begin{cases}3x-1=0\\x+2=0\end{cases}}\)
=> \(\orbr{\begin{cases}x=\frac{1}{3}\\x=-2\end{cases}}\)
#)Giải :
a) \(\left(3x-5\right)^2-\left(x+1\right)^2=0\)
\(\Leftrightarrow\left(3x-5+x+1\right)\left(3x-5-x-1\right)=0\)
\(\Leftrightarrow\left(4x-4\right)\left(2x-6\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}4x-4=0\\2x-6=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=3\end{cases}}}\)
b) \(\left(5x-4\right)^2-49x^2=0\)
\(\Leftrightarrow\left(5x-4\right)^2-\left(7x\right)^2=0\)
\(\Leftrightarrow\left(5x-4-7x\right)\left(5x-4+7x\right)=0\)
\(\Leftrightarrow\left(-2x-4\right)\left(12x-4\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}-2x-4=0\\12x-4=0\end{cases}\Rightarrow\orbr{\begin{cases}x=-2\\x=\frac{1}{3}\end{cases}}}\)
a,\(\left(3x-5+x+1\right)\left(3x-5-x-1\right)=0\)
\(\left(4x-4\right)\left(2x-6\right)=0\)
=>4x-4=0 hoặc 2x-6=0
x=1 x=3
vậy...........
b,\(\left(5x-4+7x\right)\left(5x-4-7x\right)\) =0
\(\left(12x-4\right)\left(-2x-4\right)=0\)
=>12x-4=0 hoặc -2x-4=0
x=\(\frac{1}{3}\) x=-2
vậy..........
hc tốt