Question

Oblicz.
1.a) [1-0,1x(1-0,1)^2 : 0,1
b) [(1 2/3 - 1 1/6) x 1/2]^5
c)[(5^1 + 0,5)^2 : (3^1 - 0,5^2)]^3

2.Oblicz
a) (7^3 - 8^3) - (7 - 8)^3
b) (8-2)^4 - (8^4 - 2^4)
c) (6^3 + 4^3) - (6 + 4)^3
d) (17 + 3)^2 - (17^2 + 3^2)

Answer 1

1.a) [1-0,1x(1-0,1)^2 : 0,1 = [1-0,1x+0,01x]^2:0,1 = (1-0,11x)^2:0,1 = (1+o,0121x^2)*10= 10+0,121x^2 
b) [(1 2/3 - 1 1/6) x 1/2]^5 = [(5/3-7/6)x 1/2]^5 = (3/6 x *1/2)^5 = 1/4x^5 = 0,25x^5
c)[(5^1 + 0,5)^2 : (3^1 - 0,5^2)]^3 = [5.5^2:2,5^2]^3=(30,25:6,25)^3=4,84^3=113,4

2.Oblicz
a) (7^3 - 8^3) - (7 - 8)^3 = (343 - 512) + 5^3 = -169 +125 = 294
b) (8-2)^4 - (8^4 - 2^4) = 1296 - (4096-16) = 1296-4080=-2784
c) (6^3 + 4^3) - (6 + 4)^3 = (216 + 69) - 1000 = 1285
d) (17 + 3)^2 - (17^2 + 3^2) = 400 - (289 +9)=400-298 = 102