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Daca a=√3-√6 si b=√8-3 , atunci (2a^2-b^2)^2013 .

Răspuns :

[2(√3-√6)²-(√8-3)²] ^2013=
=[2(3-2√18+6)-(8-6√8+9)]^2013=
[(2(9-6√2)-(17-12√2)^2013=
(18-12√2-17+12√2)^2013=
1^2013=1
[ 2* (√3-√6)²-(√8-3)²]²⁰¹³=[2*(3-2√18+6)-(8-6√8+9)]²⁰¹³ =(6-4√18+12-8+6√8-9)²⁰¹³=
=(1-4*3√2+6*2√2)²⁰¹³=(1-12√2+12√2)²⁰¹³=1²⁰¹³=1