Question

Repede daca puteti,multumesc :D
1.a).determinati nr nat x,astfel incat x+7 supra3=x+4 supra 2
b)determinati nr nat x,astfel incat x supra 3=4 supra x+1
c)determinati nr nat a si b,astfel incat a supra 5=1 supra b+1
d)determinati nr nat n,astfel incat 2 la puterea n+1 supra 9=8 supra 3 la puterea n
e).determinati nr nat n,astfel incat 5 la puterea n supra 13 la puterea n=7 la puterea n supra 11 la puterea n.
2.aratati ca daca a supra 3=b supra 2 atunci(14a-21b+1)la puterea 2013=1

Answer 1

1.a).determinati nr nat x,astfel incat x+7 supra3=x+4 supra 2
(x+4)/3=(x+4)/2
2x+14=3x+12
x=2
b)determinati nr nat x,astfel incat x supra 3=4 supra x+1
x/3=4/(x+1)
x²+x=12
x²+x-12=0
x²-3x+4x-12=0
x(x-3)+4(x-3)=0
(x-3)(x+4)=0
x=3
x=-4
 c)determinati nr nat a si b,astfel incat a supra 5=1 supra b+1
a/5=1/(b+1)
a(b+1)=5
solutia 1
a=5
b+1=1
b=0
solutia 2
a=1
b+1=5
b=4

d)determinati nr nat n,astfel incat 2 la puterea n+1 supra 9=8 supra 3 la puterea n
2^(n+1)/9=8/3^n
2^(n+1)/3²=2³/3^n
2^(n+1) * 3^n=2³ * 3²
 3^n= 3²
n=2
2^(n+1) =2³
n+1=3  n=2

 e).determinati nr nat n,astfel incat 5 la puterea n supra 13 la puterea n=7 la puterea n supra 11 la puterea n.
5^n/13^n=7^n/11^n
n=0
1/1=1/1
1=1

2.aratati ca daca a supra 3=b supra 2 atunci(14a-21b+1)la puterea 2013=1
a/3=b/2
2a=3b
14a=21b
(14a-21b+1)²⁰¹³=1²⁰¹³=1