Докажите, что: 2/(√3+1)+1/(√3+2)+1/√2=1+√2/2.

Question

Докажите, что: 2/(√3+1)+1/(√3+2)+1/√2=1+√2/2.

Answer 1

[2(V3+2)+(V3+1)]/[(V3+1)(V3+2)]+V2/2=
[2V3+4+V3+1]/[(V3+1)(V3+2)]+V2/2=
[3V3+5]/[(3+V3+2V3+2)]+V2/2=
[3V3+5]/[3V3+5]+V2/2=
1+V2/2