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\(\Leftrightarrow45x-90-10x+50=15-12x+36\)
=>35x-40=-12x+51
=>47x=91
hay x=91/47
a) \(\left(x+5\right)^2-x^2=45\)
\(\Leftrightarrow\)\(\left(x+5-x\right)\left(x+5+x\right)=45\)
\(\Leftrightarrow\)\(5\left(x^2+5\right)=45\)
\(\Leftrightarrow\)\(x^2+5=\frac{45}{5}=9\)
\(\Leftrightarrow\)\(x^2=9-5=4\)
\(\Leftrightarrow\)\(x^2=2^2\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)
b) \(\left(2x-3\right)^2-\left(2x+1\right)^2=3\)
\(\Leftrightarrow\)\(\left(2x-3-2x-1\right)\left(2x-3+2x+1\right)=3\)
\(\Leftrightarrow\)\(-4\left(4x-2\right)=3\)
\(\Leftrightarrow\)\(-8\left(2x-1\right)=3\)
\(\Leftrightarrow\)\(2x-1=-\frac{3}{8}\)
\(\Leftrightarrow\)\(2x=-\frac{3}{8}+\frac{8}{8}=\frac{5}{8}\)
\(\Leftrightarrow\)\(x=\frac{5}{16}\)
a) \(\left(x+5\right)^2-x^2=45\)
\(\Rightarrow x^2+2\times5x-x^2=45\)
\(\Rightarrow10x=45\)
\(\Rightarrow x=45\div10=4,5\)
Vậy giá trị của x là 4,5
b) \(\left(2x-3\right)^2-\left(2x+1\right)^2=3\)
\(\Rightarrow\left(2x-3+2x+1\right)\left(2x-3-2x-1\right)=3\)
\(\Rightarrow\left(4x-2\right)\left(-4\right)=3\)
\(\Rightarrow-16x+8=3\)
\(\Rightarrow-16x=-5\)
\(\Rightarrow x=\frac{5}{16}\)
Vậy giá trị của x là \(\frac{5}{16}\)
\(\dfrac{45}{x-5}-\dfrac{45}{x}=\dfrac{3}{2}\\ \Leftrightarrow\dfrac{1}{x-5}-\dfrac{1}{x}=\dfrac{1}{30}\\ \Leftrightarrow\dfrac{x-\left(x-5\right)}{x\left(x-5\right)}=\dfrac{1}{30}\\ \Leftrightarrow\dfrac{5}{x^2-5x}=\dfrac{1}{30}\\ \Leftrightarrow x^2-5x=600\\ \Leftrightarrow x^2-5x-150=0\\ \Leftrightarrow\left(x+10\right)\left(x-15\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-10\\x=15\end{matrix}\right.\left(t.m\right)}\)
what der were