Question

Oblicz:

1) 1 : (1+√2+√3) = ...

2) 1 : (2+√5+2√2+√10) = ...

Answer 1

1:(1+√2+√3)=1(1+√2-√3):[(1+√2+√3)(1+√2-√3)=

(1+√2-√3):(1+2√2+2-3)=(1+√2-√3):2√2=

[(1+√2-√3)√2]:[2√2×√2]=(√2-2√3+2)/4

 

1:(2+√5+2√2+√10)=

[(2+√5)-(2√2+√10)]:[(2+√5)+(2√2+√10)] [ (2+√5)-(2√2+√10)]=

[2+√5-2√2-√10]:[(2+√5)²-(2√2+√10)²]=

[2+√5-2√2-√10]:[4+4√5+5-8-8√5-10]=

[2+√5-2√2-√10]:[-9-4√5]=

[(2+√5-2√2-√10)(-9+4√5)]:[(-9+4√5)(-9-4√5)]=

[-18+8√5-9√5+20+18√2-8√10+9√10-20√2]:(81-80)=

√10-√5-2√2+2