Question

a=(√2-1)(1+√2)²
b=(-6+2²)² - √(a-√2)²
a) aratati ca a=√2+1
b) comparati numerele a si b

Answer 1

a) a=(√2-1)(1+2√2+2)= (√2-1)(2√2+3)=4+3√2-2√2-3=√2+1
b) b=(-6+4)²-√(√2+1-√2)²
b=4-1=3 
a            <            b
√2+1       <           3 /-1
√2           <           2
√2           <          √4

Answer 2

[tex]a)( \sqrt{2}-1)(1+ \sqrt{2})^2=( \sqrt{2}-1)(1+2\sqrt{2}+2)=( \sqrt{2}-1)(3+2 \sqrt{2}) \\ =3 \sqrt{2} +4-3-2 \sqrt{2}= \sqrt{2} +1 \\ b) (-6+2^2)^{2}- \sqrt{(a- \sqrt{2} })^{2}= 4-a+ \sqrt{2}=4-\sqrt{2} -1+\sqrt{2}=3 \\ \sqrt{2}+1 \ \textless \ 3 \\ adica \\ a\ \textless \ b[/tex]