Question

Numai ex. 1,2,3,4,5.
Multumesc!

Answer 1

1.(5/√18 +3/4√2 -7/√72) : 15/8√2 =
=(5/3√2 +3/4√2 -7/6√2) × 8√2/15 =
=(5*4+3*3-7*2)/12√2 × 8√2/15 =
=(29-14)/3 × 2/15 =
=15/3 × 2/15 =2/3

2.
1+3+5+...+(2x-1)=100
formula pentru suma numerelor impare   ,  cu   x termeni 
( 1 + 2x -1 ) * x / 2  =100 
2x * x / 2 =100 
2x² / 2 = 100 
x² =100 
x = 10 
(verificare 1 + 3 + 5 + .. + 19 =  100 )


3.
a=n(n+1)(n+2)(n+3)+1=[n(n+3)][(n+1)(n+2)]+1=(n²+3n)(n²+3n+2)+1=
notam n²+3n=x
=x(x+2)+1=x²+2x+1=(x+1)²

4.x²-√12=√(2√3-4)²
x²-2√3=√(2√3-4)²
√(2√3-4)²=I2√3-4I=4-2√3
x²-2√3=4-2√3
x²=4   ⇒ x=2   si  x=-2


5.
x=2
a=I√3-xI-I√3-2xI=I√3-2I-I√3-4I=2-√3-4+√3=-2
I√3-2I   √3-2<0  I√3-2I=-(√3-2)=2-√3
I√3-4I   √3-4<0  I√3-4I=-(√3-4)=4-√3