Question

Fie numerele a =√2-1 si b=√2 +1
a)Calculati aori b si a² +b²
b)Determinati media aritmetica si media geometrica a numerelor a si b
c)Indicati un numar rational si unul irational din intervalul (a,b)

Answer 1

$a= \sqrt{2} -1\\b= \sqrt{2} +1\\a) a*b=( \sqrt{2} -1)( \sqrt{2} +1)=2+ \sqrt{2} - \sqrt{2} -1=1\\ (a+b)^{2} = (2 \sqrt{2} )^{2} \\ a^{2} + b^{2} +2ab=8\\ a^{2} + b^{2} =8-2=6\\b)Ma= \frac{a+b}{2} =\frac{2\sqrt{2}}{2}=\sqrt{2}\\Mg= \sqrt{a*b} = \sqrt{1} =1\\c)Irational:\sqrt{2}\\Rational:1$