Задуманы два натуральных числа. Найдите эти числа, если их произведение равно 48...

December 2021 1 108 Report

Задуманы два натуральных числа. Найдите эти числа, если их произведение равно 48, а их сумма равна 16 пожалуйста можно без дискриминанты

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х,у- N

система уравнений:

$x + y = 16 \\ x \times y = 48$

решим методом подстановки

$x = 16 - y \\ x \times y = 48$

$(16 - y)y = 48 \\ 16y - y {}^{2} = 48 \\ - {y}^{2} + 16y - 48 = 0 \\ {y}^{2} - 16y + 48 = 0 \\ y {}^{2} - 4y - 12y + 48 = 0 \\ y(y - 4) - 12(y - 4) = 0 \\ (y - 4)(y - 12) = 0 \\ y = 4 \\ y = 12$

$x = 16 - y \\ x = 16 - 4 \\ x = 16 - 12 \\ x = 12 \\ x = 4$

ОТВЕТ: (х1, у1)= 12, 4 ; (х2, у2)= 4, 12.

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karimovartem853 Спасибо!!!

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