Đáp án: `↓`
Giải thích các bước giải:
`a, (x - 4) ² - 25 = 0`
`(x-4)²= 25`
`(x-4)²= (±5)²`
\(\left[ \begin{array}{l}x-4=5\\x-4=-5\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=9\\x=-1\end{array} \right.\)
___________
`b, ( 3x - 7) ² - 4(x+1) ²=0`
`9x²-42x+49-4(x²+2x+1)=0`
`9x²-42x+49-4x²-8x-4=0`
`5x²-50x + 45 = 0 `
`5(x²-10x+9)=0`
`5(x²-x-9x+9)=0`
`5[(x²-x)-(9x-9)]=0`
`5[x(x-1)-9(x-1)]=0`
`5(x-1)(x-9)=0`
\(\left[ \begin{array}{l}x-1=0\\x-9=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=1\\x=9\end{array} \right.\)
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`c, x ³ + x ² + x +1 = 0`
`(x³+x)+(x²+1)=0`
`x(x²+1)+(x²+1)=0`
`(x²+1)(x+1)=0`
\(\left[ \begin{array}{l}x^2+1=0\\x+1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x^2=-1(loại)\\x=-1\end{array} \right.\)
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`d, x ³+x ² - x - 1= 0`
`(x³-x)+(x²-1)= 0`
`x(x²-1)+(x²-1)=0`
`(x²-1)(x+1)=0`
`(x+1)(x-1)(x+1)=0`
`(x+1)²(x-1)=0`\(\left[ \begin{array}{l}(x+1)^2=0\\x-1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=-1\\x=1\end{array} \right.\)
________________
`e, (2x - 1) ³ - 4(x ²+1) (2x -1) = 0`
`(2x-1){(2x-1)²-[4(x²+1)]}=0`
`(2x-1)[4x²-4x+1-(4x²+4)]=0`
`(2x-1)(4x²-4x+1-4x²-4)=0`
`(2x-1)(-4x-3)=0`
`\(\left[ \begin{array}{l}2x-1=0\\-4x-3=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=1/2\\x=-3/4\end{array} \right.\)
___________________
`f, (x+4) (5x+9) - x ² + 16 = 0`
`(x+4) (5x+9)-(x²-16)=0`
`(x+4) (5x+9)-(x-4)(x+4)=0`
`(x+4)[(5x+9)-(x-4)]=0`
`(x-4)(5x+9-x+4)=0`
`(x-4)(4x+16)=0`
\(\left[ \begin{array}{l}x-4=0\\4x+16=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=4\\x=-4\end{array} \right.\)
Chúc bn học tốt !!!!
~Giang~
