Question

4. Fie numerele
$a = \sqrt{2 - \sqrt{2} }$
Si
$b = \sqrt{2 + \sqrt{2} }$
a) calculati a . b
b) calculati
$(a + b) {}^{2}$
c) Aratati ca
$\frac{b}{a} - \sqrt{2} \: \: \: \: \: eq$
​

Answer 1

Răspuns:

a)

a·b=√(2-√2)·√(2+√2)=

√(2-√2)(2+√2)=√4-2=√2

b)(a+b)²=(√√2-√2+√(2+√2)]²=

(√2-√2))²+√(2+√2)²+2(√2-√2)√(2+√2)=

2-√2+2+√2+2√2=4+2√2

______________________

c)b/a=√(2=√2)/√(2+√2)= amplifici   fractia   cu √(2+√2)=

√(2+√2)²/(√2-√2)(√2-√2)=

2+√2)/√2=√2+1

√2+1-√2=1∈Q

Explicație pas cu pas: