the sum of two positive numbers is 7 times their 差. the 差 of the squares of these numbers is twice the sum of the numbers. find these numbers

解

t h e s u m o f tw o p os i t i v e n u mb ers i s 7 t im es t h e i r d i ff ere n ce . t h e d i ff ere n ce o f t h e s q u a res o f t h ese n u mb ers i s tw i ce t h e s u m o f t h e n u mb ers . f in d t h ese n u mb ers

The numbers : 8, 6

解答ステップ

Represent the numbers with

x and y

number 1 : x

number 2 : y

A.T.Q.:

x + y = 7 (x - y)

x^{2} - y^{2} = 2 (x + y)

equation系を解く:

x + y = 7 (x - y), x^{2} - y^{2} = 2 (x + y) : (x = 8, x = 0, y = 6 y = 0)

Select positive solutions:

6, 8

The numbers : 8, 6