F.3 Maths Questions 40pts.

Q1 2(x+2a)^2 - a(x+2a) - a^2 = 0

Let y be x+2a :

2y^2 - ay - a^2 = 0

(2y + a)(y - a) = 0

y = - a/2 or y = a

x+2a = -a/2 or x+2a = a

x = -a/2 - 2a =-5a/2
or x = a - 2a = - a

Q2 2^(n+4) - 3(2^(n+3)) ] / 2^(n+2)

= (2^n) [ 2^4 - 3(2^3) ] / [(2^n)(2^2)]

= (16 - 24) / 4

= - 2

Q3 y^2 - 13y + 36

= (y - 4)(y - 9)

x - 13√x + 36 = 0

Let y = √x :

(√x - 4)(√x - 9) = 0

√x = 4 or √x = 9

x = 16 or x = 81