Question

Determinati numerele x si y stiind ca :
a) sunt invers proportionale cu 2 si 3 , iar x-y =10
b) sunt invers proportionale cu 2 si 3, iar x (la puterea a 2a) + y (la puterea a 2 a)= 208
c) sunt invers proportionale cu 3 si 4, iar x( puterea a2a) - y ) la puterea a 2 a )=175

Answer 1

a)
x=k/2
y=k/3
x-y=10
k/2-k/3=10
3k-2k=60
k=60
x=k/2=60/2=30
y=k/3=60/3=20

b) 
x=k/2
y=k/3
x²+y²=208
(k/2)²+(k/3)²=208
k²/4+k²/9=208
9k²+4k²=7488
13k²=7488
k²=7488:13=576
k=√576=24
x=k/2=24/2=12
y=k/3=24/3=8

c)
x=k/3
y=k/4
x²-y²=175
(k/3)²-(k/4)²=175
k²/9-k²/16=175
16k²-9k²=25200
7k²=25200
k²=25200:7=3600
k=√3600=60
x=k/3=60/3=20
y=k/4=60/4=15