Question

Comparati numerele a si b
a=(√2-1)(1+√2)²
b=(-6+2²)²-√(1-√2)²

Answer 1

A il scrii sub forma de : (radical(2) - 1) * (radical(2) + 1) * (radical(2) + 1) , primele 2 paranteza reprezinta formula (a-b)*(a+b)= a^2 - b^2 , inlocuim si obtinem (2-1)*(radical(2)+1) = radical(2) + 1.
B calculezi prima paranteza -6 + 4 = 2,
2*2= 4, a doua paranteza observi ca e radical sub putere, deci, o scrii ca |1-radical(2)| = radical(2) - 1 , acum B= 4 - (radical(2)-1) = 5 - radical(2) radical(2)~ 1,44 => A~2,44 iar B~3,56 B>A

Answer 2

a=2-2=0
b=36+(-48)+8-√1-2√2+2=44+(-48)-1-12+2= -4-1-12+2=-15
a>b