Page 119 - Algebra

Explanation
1. x2 – 6√3x + 15
Split the middle term
= x2 – 5√3x – √3x + 15
= x (x –5√3) – √3 (x – 5√3) = (x –√3) (x –5√3)
2. x4+64
Add and subtract 16x2
=x4 +64+16x2–16x2
=(x2 + 8)2 – (4x)2
Use the identity a2 – b2 = (a + b) (a – b) =(x2 +8–4x)(x2 +8+4x)
3. 3.9 can be written as (4 – 0.1)2
Use the identity, (a – b)2= a2 – 2ab + b2 (4–0.1)2 =42 –2×4×0.1+0.12
= 16 – 0.8 + 0.01 = 15.21
4. (x2+4)(x2 –4)+16
Use the identity, (a + b) (a – b) = a2 (x2)2 – 42 + 16
x4– 16 + 16
x4
5. Add 2 on both side x4 + 1 +2=119+2
Using the identity x2 + 1 = (x + 1 )2 – 2
– b2
𝑥4
𝑥2 𝑥
(x2 + 1 )2= 121 𝑥2
x2+1 =11 𝑥2
Subtract 2 from both sides
21
x+ –2=11–2
𝑥2
12 (x– )=9
1
𝑥
16x + 8 ×
- 6 × 5 = 300
𝑥
x– =3
6. Let the salary of one day be x
𝑥
2
16x + 4x – 30 = 300
20x = 330
x = $16.5
Salary paid to an electrician for 30 days = 16.5 × 30 = $495
Page 118 of 177
Algebra I & II