Question

Proszę o pomoc zadania w załączniku

Answer 1

3.

a)
 = √8(√9 + √4 + √1) = √(4*2)(3 + 2 + 1) = 6√4 * √2 = 12 * √2

b)
= 2√(25*3) - 2√3 + √(3*100) = 10√3 - 2√3 + 10√3 = 20√3 - 2√3 = 18 * √3

c)
= ∛(2*27) + ∛(2*64) + ∛(2*216) = ∛(2*3³) + ∛(2*4³) + ∛(2*6³) = ∛2*(3+4+6) =

= 13 * ∛2

d)
= ∛(2*500) - ∛(2*4) = ∛1000 - ∛8 = ∛10³ - ∛2³ = 10 - 2 = 8

e)
= [4√3 + √(3*9)]/√(4*3) = (4√3 + 3√3)/2√3 = 7/2 = 3,5

f)
= √2*(√(2*3) + √(6*4))/√3 = √2*(√(2*3) + 2*√(2*3))/√3 =

= √(2)*3√(2)*√(3))/√3 = 2*3 = 6

4.

a)
= -∛(125/64) + ∛(27/8) - ∛(243/32) = -5/4 + 3/2 - ∛(27*9/8*4) =

= 1/4 - (3/2)*∛(9/4) = 0,25 - 1,5  * ∛2,25


b)
= -∛(2/3)³ - ∛(6/5)³ + ∛(27*9/8*4) = -2/3 - 6/5 + (3/2)*∛(9/4) =

= -28/15 + 1,5 * ∛2,25

c)

= -∛(9/4)∛(3/2) + ∛(16/9)∛(4/3) =-∛(27/8)+∛(64/27) = - 3/2 + 4/3 = -1/6


d)
= - ∛(750/6) - ∛(216) - ∛(320/5) = - ∛(125) - ∛(216) - ∛(64) =

= - 5 - 6 - 4 = -15

5.
a)
x = (3³²-3³⁰)/3²⁸ = 3³⁰*(3²-1)/3²⁸ = 3²*(9-1) = 9*8 = 72

n-1 ≤ x < n
n-1 ≤ 72 < n
72 < 73
n = 73

b)
x = (2²²+2²¹)/(3*2¹¹) = 2²¹(2+1)/(3*2¹¹) = 2¹⁰*3/3 = 2¹⁰ = 1024
n-1 ≤ x  < n
n-1 ≤ 1024 < n
1024 < 1025
n = 1025

c)
x = (5¹⁴-5¹³)/(5¹³+5¹²) = (5¹³)(5-1)/(5¹²*(5²+1)) = 5*4/26 = 20/26 = 10/13
=5*4/26 = 20/26

n-1 ≤ 20/26 < n
20/26 < 1
n = 1