Question

The summation of two numbers is 7 and the difference of their squares is 7. What is the difference of the numbers?​

Answer 1

Answer:

X-y=7

x^2-y^2=45

(7+y)^2-y^2=45

49+14y+y^2-y^2=45

14y=45–49

y=-4/14

y=-2/7

x=7+(-2/7)

x=47/7

Sum is (47/7)+(-2/7)=45/7

Alternatively,

y-x=7

y=7+x

x^2-(7+x)^2=45

-49–14x=45

-14x=94

x=-47/7

Sum is also (-47/7)+(7+(-47/7)) = -47/7+49/7–47/7 = 49/7

Sum is also -45/7 and -49/7 (Look at the work shown by the others). There are four sums because the differences don’t necessarily have x and y in similar positions compared to the two starting equations.