Question

Prove que D = √[(1 + √5) ÷ 2 - (1 - √5) ÷ 2]² + [(3 + √5) ÷ 2 - (3 - √5) ÷ 2]²

D = √10

detalhadamente por favor!! muito obrigado

Answer 1

D=√[(1+√5)×1/2-(1-√5)×1/2]²+
[(3+√5)×1/2-(3-√5)×1/2]²

D= √[(1+√5/2)-(1-√5/2)]² +
[(3+√5/2)-(3-√5/2)]²

D= √[1+√5/2-1+√5/2]²+[3+√5/2-3+√5/2]²

D= √[√5/2+√5/2]² + [√5/2+√5/2]²

D= √ [2√5/2]² + [2√5/2]²

D= √ [√5]² + [√5]²

D= √ 5 + 5

D= √10