решите неравенство 7х^4-48х^2-7=0. Created by aibraeva02. matematika-ru

решите неравенство 7х^4-48х^2-7=0...

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$7 {x}^{4} - 48 {x}^{2} - 7 = 0 \\ \\ 7 {x}^{4} - 49 {x}^{2} + {x}^{2} - 7 = 0 \\ \\ 7 {x}^{2} ( {x}^{2} - 7) + ( {x}^{2} - 7) = 0 \\ \\ (7 {x}^{2} + 1)( {x}^{2} - 7) = 0 \\$

1) 7x² + 1 = 0

7x² = - 1

x² = - 1 / 7

Не имеет действительных корней (∅)

2) х² - 7 = 0

х² = 7

х = - √7

х = √7

ОТВЕТ: - √7 ; √7

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армения20171 7x⁴-48x²-7=0
x²=t>0
7t²-48t-7=0

D/4=576+49=625=25²

t=(24±25)/7
t1=7;t2=-1/7
1)x²=7;x=±√7
2)x²=-1/7;x€∅
ответ х=±√7

2 votes Thanks 1

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