Question

В арифметической прогресии
{a2+a4=16
{a1*a5=28
Найдите: a1 и d

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Answer 1

Объяснение:

$\left \{ {{a_2+a_4=16} \atop {a_1*a_5=28}} \right. \ \ \ \ \left \{ {{a_a+d+a_1+3d=16} \atop {a_1*(a_1+4d)=28}} \right.\ \ \ \ \left \{ {{2a_1+4d=16} \atop {a_1*(a_1+4d)=28}} \right.\ \ \ \ \left \{ {{4d=16-2a_1} \atop {a_1*(a_1+16-2a_1)=28}} \right. \\\left \{ {{4d=16-2a_1} \atop {a_1*(16-a_1)=28}} \right. \ \ \ \ \left \{ {{4d=16-2a_1\ |:4} \atop {16a_1-a_1^2=28}} \right.\ \ \ \ \left \{ {{d=4-0,5a_1} \atop {a_1^2-16a+28=0}} \right. \ \ \ \ \left \{ {d=4-0,5a_1} \atop {D=144\ \ \sqrt{D}=12 }} \right$

$\left \{ {{d=3\ \ d'=-2} \atop {a_1=2\ \ a_1'=14}} \right. .$

ответ: a₁=2   d=3;     a₁'=14    d'=-2.