Вопрос школьника по предмету Математика
при сложении суммы , разности, произведения и частного двух натуральных чисел получили 441 . чему равны эти два числа . решить с применением формулы (a+b)^2=a^2+2ab+b^2. Пожалуйста!
Ответ учителя по предмету Математика
Пусть x — первое число, y — второе число; x,y∈N
Тогда: x+y+x-y+xy+x/y = 441
Приводишь подобные: 2x+xy+x/y = 441
2xy+xy²+x = 441y
x(y²+2y+1) = 441y
x(y+1)² = 441y
x(y+1)² = 21²y
x/y = (21/(y+1))²
Если x/y — натуральное, то решением этого уравнения являются 2 пары натуральных чисел: (98; 2) и (54 ; 6)
Подставляешь найденные пары чисел в уравнение: 2x+xy+x/y = 441
И получаешь, что условию удовлетворяют пара натуральных чисел: (98; 2)
x=98 ; y=2
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