Question

Find two rational numbers which differ by 3 and the sum of whose squares is 117

Answer 1

The two rational numbers are -6&-9 or 6&9

Answer 2

Answer:

Answer: -6,-9 or 6,9

Step-by-step explanation:

Let the numbers be x and x-3

Then,

x^2+(x-3)^2=117

x^2+x^2+9-6x=117

2x^2-6x-108=0

x^2-3x-54=0

x^2-9x+6x-54=0

x(x-9)+6(x-9)=0

(x-9)=0 or (x+6)=0

x=9 or x= -6

Difference:-

x=9

y=9-3

=6

or

x= -6

y= -6-3

= -9