Question

1)Determinati numarul  real a  stiind ca 2 este solutia ecuatiei 2x(a+3)-3ax=18
2)Calculati √(2-√5)²+√(3√3-6)²+·√(-√5-1)²:

Answer 1

1)2ax+6 -3ax=18

-ax=18-6
-ax=12
ax=12

x=2

a*2=12
a=6

2)|2-√5| + |3√3-6| + | -√5-1|= -2+√5 -3√3 +6 -|√5+1|=

= 4 + √5 -3√3 -√5 -1=

=4 -3√3 -1=

= 3-3√3=  3(1-√3)

Answer 2

1)
x = 2
2x(a + 3)-3ax = 18
-------
2ax + 6x - 3ax = 18
-ax + 6x = 18
x(6 - a) = 18
dar x = 2
=> 2(6 - a) = 18
6-a = 18 / 2
6 - a = 9
a = 6 - 9
a = -3
Proba:  
x = 2 si a = -3
2x(a + 3) - 3ax = 18
2 * 2 * (-3 + 3) - 3 * (-3) * 2 = 4 * 0 + 9 * 2 = 18  corect.

2)
√(2-√5)²+√(3√3-6)²+·√(-√5-1)² = 
= 2 - √5 + 3√3-6 + √5 + 1 =
= 3√3 + 2 - 6 + 1 =
= 3√3 - 3 = 3(1 - √3)