Question

Se a2 + b2 =30 e ab = 15, qual o valor de (a+b) 2?

Answer 1

Resposta:

Explicação passo a passo:

$Dados:$

$a^{2} +b^{2} =30$

$ab=15$

$(a+b)^{2} =a^{2}+2ab+b^{2}$

$(a+b)^{2} =(a^{2}+b^{2})+2ab$

$(a+b)^{2} =30+2.(15)$

$(a+b)^{2} =30+30$

$(a+b)^{2} =60$

Answer 2

a

2

+b

2

=30

ab=15ab=15ab=15

(a+b)2=a2+2ab+b2(a+b)^{2} =a^{2}+2ab+b^{2}(a+b)

2

=a

2

+2ab+b

2

(a+b)2=(a2+b2)+2ab(a+b)^{2} =(a^{2}+b^{2})+2ab(a+b)

2

=(a

2

+b

2

)+2ab

(a+b)2=30+2.(15)(a+b)^{2} =30+2.(15)(a+b)

2

=30+2.(15)

(a+b)2=30+30(a+b)^{2} =30+30(a+b)

2

=30+30

(a+b)2=60(a+b)^{2} =60(a+b)

2

=60