Question

Aratati ca numarul a= $\sqrt{9+2\sqrt{14} }$ - $\sqrt{3+2\sqrt{2} }$ + $\sqrt{16-6\sqrt{7} }$ este rational.

Answer 1

Răspuns:

9+2√14=7+2+2√14=(√7²+2√14+√2²)=

(√7+√2)²

√(7+√2)²=√7+√2

3+2√2=2+1+2√2=√2²+2√2+√1²=

(√2+1)²

√(2+1)²=√2+1

16-6√7=9-6√7+7=

3²-6√7+√7²=

(3-√7)²=

√(3-√7)²=3-√7

a=√7+√2-(√2+1)=3-√7=

√7+√2-√2-1+3-√7=2∈Q

Explicație pas cu pas: