张灵谱
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求下列各式中x的值：
1、 \(\displaystyle {{x}^{2}}=256\)
解：∵ \(\displaystyle {{x}^{2}}=256\)
∴ \(\displaystyle x=\pm \sqrt{{256}}\)
∴ \(\displaystyle x=\pm 16\)
2、\(\displaystyle 81{{x}^{2}}-49=0\)
解 ∵ \(\displaystyle 81{{x}^{2}}-49=0\)
∴ \(\displaystyle 81{{x}^{2}}=49\)
\(\displaystyle {{x}^{2}}=\frac{{49}}{{81}}\)
\(\displaystyle x=\pm \sqrt{{\frac{{49}}{{81}}}}\)
\(\displaystyle x=\pm \frac{7}{9}\)
3、\(\displaystyle {{\left( {2x-1} \right)}^{2}}={{\left( {-5} \right)}^{2}}\)
解：∵ \(\displaystyle {{\left( {2x-1} \right)}^{2}}={{\left( {-5} \right)}^{2}}\)
∴ \(\displaystyle {{\left( {2x-1} \right)}^{2}}=25\)
\(\displaystyle 2x-1=\pm \sqrt{{25}}\)
\(\displaystyle 2x-1=\pm 5\)
即：\(\displaystyle 2x-1=5\)或\(\displaystyle 2x-1=-5\)
∴ \(\displaystyle x=3\)或\(\displaystyle x=-2\)
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