Page 100 - Algebra

Explanation:
1. Divide the power of both the sides by 4
𝑎1 204 = 814
𝑎 4×1 204=3 4
𝑎
204 =31
Now multiply both the sides by 202
𝑎
204 . 20 = 3 .20
212 20𝑎+2 = 3 × 400
4 4
4x = 64 and 9(x+y) = 6561
22x = 26 and 9(x+y) = 94
As the bases are the same, you can equate the bases 2x = 6 and (x + y) = 4
x= 3
Put x = 3 in x + y = 4
3+y=4
y=1
So, x – y = 3 – 1 = 2
3. Put a = 1
(√𝑥 + 1 ) = 2(x – 2) 1
(𝑥+1)2 =2(x–2)
Square both the equations x + 1 = 4(x – 2)2
x + 1 = 4(x2 – 4x + 4)
x + 1 = 4x2 – 16x + 16
4x2 – 16x + 16 – x – 1 = 0
4x2 – 17x + 15 = 0
4x2 – 12x – 5x + 15 = 0 4x(x – 3) – 5(x – 3) = 0 (4x – 5)(x – 3) = 0
x = 3 or 5 4
20𝑎+2 = 1200
2. Simplify the exponential equation
Page 99 of 177
Algebra I & II