Problem / game
First name
Amrit Cassim
School
Hymers College
Country
Age
14
solution for h)
1 Multiplying by sqrt(c)+d, we get
2 sqrt(a)+b=(sqrt(a)+b)(sqrt(c)-d)(sqrt(c)+d)
3 sqrt(a)+b=(sqrt(a)+b)(c-(d^2))
4 We have a common factor of sqrt(a)+b on both sides so we divide by it
5 1=c-(d^2)
6 Adding (d^2) to both sides we get
7 c=(d^2)+1
8 This shows that any positive value for a and b can be chosen, but the values of 9 c and d must be chosen so that they obey the constraint in line 7