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smeyilya
@smeyilya
August 2022
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решите уравнение x^2+2x+2/x+1/=7, выполнив замену переменной.
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sharadi
x²
+2x+2|x+1|=7
x²+2x+ 1 +2|x+1| = 8
(x +1)² +2|x+1| = 8
|x+1| = y
y² +2y =8
y² +2y -8 0
По т. Виета корни -4 и 2
а) у = -4 б) у = 2
|x +1| = -4 | x +1| = 2
∅ х +1 = 2 или х +1 = -2
х = 1 х = -3
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Answers & Comments
x²+2x+ 1 +2|x+1| = 8
(x +1)² +2|x+1| = 8
|x+1| = y
y² +2y =8
y² +2y -8 0
По т. Виета корни -4 и 2
а) у = -4 б) у = 2
|x +1| = -4 | x +1| = 2
∅ х +1 = 2 или х +1 = -2
х = 1 х = -3