Question

Fie a=radical din 2+1,b=radical din3+1 ,calculeaza:a+b ;a-b / (a+b)(a-b)

Answer 1

5+1+9=57282828282828

Answer 2

a=√2 +1
b=√3+1
a+b= √2+1+√3+1= √2+√3+2
a-b= √2+1-√3-1= √2-√3
(a+b)(a-b) = (√2+√3+2)(√2-√3) =2-√6+√6-3+2√2-2√3=-1+2√2-2√3
a-b/ (a+b)(a-b) = 1/(a+b)= 1/(√2+√3+2)=(√2+√3-2)/ (√2+√3)²-2²=
=(√2+√3-2) / (2+3+2√6-4) = (√2+√3-2)/ (1+2√6)=
= (√2+√3-2)(2√6-1)/(2²*6-1) = (2√12-√2+2√18-√3-4√6+2) / 23=
=(4√3-√2+6√2-√3-4√6+2)/ 23=
=(3√3+5√2-4√6+2) / 23