maths. x6Q

1. k2 = 16k
k2 - 16k = 0
k(k - 16) = 0
k = 0 or k - 16 = 0
k= 0 or k =16
2. 9y2 - 16 = 0
(3y + 4)(3y - 4) = 0
3y + 4 = 0 or 3y - 4 = 0
y = -4/3 or y = 4/3
3. 2t2 + 5t + 3 = 0
2t2 + 3t + 2t + 3 = 0
t(2t + 3) + (2t + 3) = 0
(2t + 3)(t + 1) = 0
2t + 3 = 0 or t + 1 = 0
t = -3/2 or t = -1
4. (a - 2)(a + 2) = 15a/2
a2 - 4 - 15a/2 = 0
2a2 - 15a - 8 = 0
2a2 + a - 16a - 8 = 0
a(2a + 1) - 8(2a + 1) = 0
(a - 8)(2a + 1) = 0
a - 8 = 0 or 2a + 1 = 0
a = 8 or a = -1/2
5. (4 - x)2 - 5(4 - x) - 14 = 0
Let 4 - x = u
u2 - 5u - 14 = 0
u2 - 7u + 2u - 14 = 0
u(u - 7) + 2(u - 7) = 0
(u + 2)(u - 7) = 0
(4 - x + 2)(4 - x - 7) = 0
(6 - x)(-x - 3) = 0
6 - x = 0 or - x - 3 = 0
x = 6 or x = -3
6. (2x + 3)2 = x(2x + 3)
(2x + 3)2 - x(2x + 3) = 0
(2x + 3)(2x + 3 - x) = 0
(2x + 3)(x + 3) = 0
2x + 3 = 0 or x + 3 = 0
x = -3/2 or x = -3

1. k^2=16k
k^2－16k=0
k(k－16)=0
k=0 or k=16

2. 9y^2－16=0
(3y－4)(3y+4)=0
y=4/3 or y=－4/3

3. 2t^2+5t+3=0
(2t+3)(t+1)=0
t=－3/2 or t=－1

4. (a－2)(a+2)=15a/2
a^2－4=15a/2
2a^2－8=15a
2a^2－15a-8=0
(2a+1)(a－8)=0
a=－1/2 or a=8

5. (4－x)^2－5(4－x)－14=0
(4－x－7)(4－x+2)=0
(－x－3)(6－x)=0
x=－3 or x=6

6. (2x+3)^2=x(2x+33)
4x^2+12x+9－2x^2－33x=0
2x^2－21x+9=0
x=(21+/-sqrt(369))/4
=(21+/-3sqrt(41))/4