Toán 9 Giải phương trình

7 1 2 5

7 1 2 5

Cựu TMod Toán
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19 Tháng một 2019
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5x=x+1+x−1⇔5x=2x+2x2−1⇔2x2+2x4−x2−5=0⇔2(x2−2516)+2(x4−x2−1516)=0⇔2(x−54)(x+54)+2.x4−x2−225256x4−x2+1516=0⇔2(x2−2516)(1+x2+916x4−x2+1516)=0⇔x2=2516⇔x=54\sqrt{\frac{5}{x}}=\sqrt{x+1}+\sqrt{x-1}\Leftrightarrow \frac{5}{x}=2x+2\sqrt{x^2-1}\Leftrightarrow 2x^2+2\sqrt{x^4-x^2}-5=0\Leftrightarrow 2(x^2-\frac{25}{16})+2(\sqrt{x^4-x^2}-\frac{15}{16})=0\Leftrightarrow 2(x-\frac{5}{4})(x+\frac{5}{4})+2.\frac{x^4-x^2-\frac{225}{256}}{\sqrt{x^4-x^2}+\frac{15}{16}}=0\Leftrightarrow 2(x^2-\frac{25}{16})(1+\frac{x^2+\frac{9}{16}}{\sqrt{x^4-x^2}+\frac{15}{16}})=0\Leftrightarrow x^2=\frac{25}{16}\Leftrightarrow x=\frac{5}{4}
 
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