Предмет: Алгебра, автор: sarin2011

сумма 2х натуральных чисел равна 50, а произведение на 11 меньше, чем разность их квадратов. Найдите эти числа.

пожалуйста, с подробным решением,
заранее спасибо

Ответы

Автор ответа: MySoulCry1

x+y=50
x²-y²=z
xy=z-11

Выразим z
Z=xy+11
Подставим во второе выражение
x²-y²=ху+11
Выразим х из первого
Х= 50 - у
Подставим во второе
(50-у)²-у²=50у-у²+11
Решаем
У²-150у+2489=0
У1 =19
У2=131
Х1=50-19=31
Х2=50-131=-81

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