helpppp
`a)(5x-1)(5x+1)=15`
`<=>25x^2-1=15`
`<=>25x^2=16`
`<=>x^2=16/25`
`<=>x=+-4/5`
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`b)x^2-8x+16-(5x+2)^2=0`
`<=>(x-4)^2-(5x+2)^2=0`
`<=>(x-4-5x-2)(x-4+5x+2)=0`
`<=>(-4x-6)(6x-2)=0`
`<=>[(x=-3/2),(x=1/3):}`
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`c)x^2-10x+9=0`
`<=>x^2-9x-x+9=0`
`<=>(x-9)(x-1)=0`
`<=>[(x=9),(x=1):}`
a, \(\left(5x-1\right)\left(5x+1\right)=15\)
\(\Leftrightarrow\left(5x\right)^2-1^2=15\)
\(\Leftrightarrow25x^2-1=15\)
\(\Leftrightarrow25x^2=16\)
\(\Leftrightarrow x^2=\dfrac{16}{25}=\left(\pm\dfrac{4}{5}\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
b, \(x^2-8x+16-\left(5x+2\right)^2=0\)
\(\Leftrightarrow x^2-2.x.4+4^2-\left(5x+2\right)^2=0\)
\(\Leftrightarrow\left(x-4\right)^2-\left(5x+2\right)^2=0\)
\(\Leftrightarrow\left(x-4-5x-2\right)\left(x-4+5x+2\right)=0\)
\(\Leftrightarrow\left(-4x-6\right)\left(6x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-4x-6=0\\6x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}-4x=6\\6x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
c, \(x^2-10x+9=0\)
\(\Leftrightarrow\left(x^2-9x\right)-\left(x-9\right)=0\)
\(\Leftrightarrow x\left(x-9\right)-\left(x-9\right)=0\)
\(\Leftrightarrow\left(x-9\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-9=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=9\\x=1\end{matrix}\right.\)
