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Temas1095
@Temas1095
July 2022
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Решите систему уравнений.
y-x=8
√x-√y=-2
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wejde
Verified answer
Y-x=8, √x-√y=-2
y=8+x, √x-√(8+x)=-2/()²
x-2√x*√(8+x)+8+x=4
2x+8-4=2√(x(8+x))/:2
x+2=√(8x+x²)/()²
x²+4x+4=8x+x²
4x+4=8x
8x-4x=4
4x=4/:4
x=1 ⇒ y=8+1=9
Проверим:
9-1=8, √1-√9=-2
8=8, 1-3=-2
8=8, -2=-2
Ответ: (1;9)
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Answers & Comments
Verified answer
Y-x=8, √x-√y=-2y=8+x, √x-√(8+x)=-2/()²
x-2√x*√(8+x)+8+x=4
2x+8-4=2√(x(8+x))/:2
x+2=√(8x+x²)/()²
x²+4x+4=8x+x²
4x+4=8x
8x-4x=4
4x=4/:4
x=1 ⇒ y=8+1=9
Проверим:
9-1=8, √1-√9=-2
8=8, 1-3=-2
8=8, -2=-2
Ответ: (1;9)