Question

Please Help!!!!!! Me On These Questions!!!!!

3) Diane and her sister have ages that are two 
consecutive odd integers.  Their product is 63.  
Write and solve an equation for Diane's age if she 
is the younger sister. 

5) One positive number is 4 more than the other, 
and the sum of their squares is 208. Find each 
number.

Answer 1

Consecutive odd or even integers are of the form x, x+2.
So we have x(x+2) = 63, where Diane's age = x.

x²+2x = 63.
x² + 2x - 63 = 0
(x + 9)(x - 7) = 0
x = -9, or 7.

Since -9 is awfully young, we rule it out and say Diane's age is 7, and her sister is 9.