Explicație pas cu pas:
a ) x / √10 = 2√5 / √2 + 3√2 / √5
√10x / 10 = ( 2√10 / 2 ) + ( 3√10 / 5 )
√10x / 10 = √10 + ( 3√10 / 5 )
√10x / 10 = ( 5√10 + 3√10 ) / 5
√10x / 10 = 8√10 / 5
5√10x / 10 = 8√10
5√10x = 8√10 x 10
5√10x = 80√10
x = ( 80√10 ) : ( 5√10 )
x = 16
b ) x / √15 = ( 3√5 / √3 ) + ( 2√3 / √5 )
√15x / 15 = ( 3√15 / 3 ) + ( 2√15 / 5 )
√15x / 15 = √15 + ( 2√15 / 5 )
√15x / 15 = ( 5√15 + 2√15 ) / 5
√15x / 15 = 7√15 / 5
5√15x = 105√15
x = 105√15 / 5√15
x = 21
c ) x / √15 - √60 / √27 = 3√20 / 5
√15x / 15 - ( 2√15 ) / ( 3√3 ) = ( 3 · 2√5 ) / 5
√15x / 15 - ( 2√15 ) / ( 3√3 ) = 6√5 / 5
√15x / 15 - ( 2√45 ) / 9 = 6√5 / 5
√15x / 15 - 6√5 / 9 = 6√5 / 5
3√15x - 30√5 = 54√5
3√15x = 54√5 + 30√5
3√15x = 84√5
x = ( 84√5 ) : ( 3√15 )
x = 28 / √3
x = 28√3 / 3
d ) x / √6 = 9√10 / 10 + 3√2 / √5
√6x / 6 = ( 9√10 / 10 ) + ( 3√10 / 5 )
√6x / 6 = ( 9√10 / 10 ) + ( 6√10 / 10 )
√6x / 6 = 15√10 / 10
√6x / 6 = 3√10 / 2
2√6x = 18√10
x = ( 18√10 ) : ( 2√6 )
x = 9√5 / √3
x = 9√15 / 3
x = 3√15
e ) x / √10 - ( 4√8 / √5 ) = 3√20 / 5
√10x / 10 - ( 4√40 / 5 ) = 3√20 / 5
√10x / 10 - ( 8√40 / 10 ) = 3√20 / 5
√10x / 10 - ( 16√10 / 10 ) = 6√5 / 5
√10x - 16√10 = 12√5
√10x = 12√5 + 16√10
x = 12√5 ÷ √10 + 16√10 ÷ √10
x = ( 12√5 ) / √10 + 16
