Question

A soma 3 termos que estão em Pá é 45 e o produto 1976. Determine os 8 números desta PA

Answer 1

Resposta:

[15-√(1399/15), 15, 15+√(1399/15), 15+2√(1399/15), 15+3√(1399/15), 15+4√(1399/15), 15+5√(1399/15), 15+6√(1399/15)] com r =√(1399/15)

Ou

[15+√(1399/15), 15, 15-√(1399/15), 15-2√(1399/15), 15-3√(1399/15), 15-4√(1399/15), 15-5√(1399/15), 15-6√(1399/15)], com r = -√(1399/15)

Explicação passo-a-passo:

PA

(x-r, x, x+r)

(x-r) +x+(x+r)=45

3x=45

x=45/3=15

(x-r)(x+r)x=1976

(x²-r²)x=1976

(15²-r²)15=1976

r²=15²-1976/15

r²=(3375-1976)/15

r²=1399/15

r=±√1399/15

Pa

(x-r, x, x+r)

[15-√(1399/15), 15, 15+√(1399/15)], com r =√(1399/15)

Ou

[15+√(1399/15), 15, 15-√(1399/15)], com r = -√(1399/15)