Question

obtenha três números em PA de modo que sua soma seja 9 e seu produto 15.​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm representac_{\!\!,}\tilde ao~especial~para~PA~de~3~termos}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x-r,x,x+r}}}}\end{array}}$

$\large\boxed{\begin{array}{l}\sf x-\backslash\!\!\!r+x+x+\backslash\!\!\!r=9\\\sf 3x=9\\\sf x=\dfrac{9}{3}\\\sf x=3\\\sf (x-r)\cdot x\cdot(x+r)=15\\\sf (3-r)\cdot 3\cdot(3+r)=15\\\sf (3-r)\cdot(3+r)=\dfrac{15}{3}\\\sf 9-r^2=5\\\sf r^2=9-5\\\sf r^2=4\\\sf r=\pm\sqrt{4}\\\sf r=\pm2\\\sf se~r=2\longrightarrow PA~crescente\\\sf (3-2,3,3+2)=(1,3,5)\\\sf se~r=-2\longrightarrow PA~decrescente\\\sf(3-(-2),3,3+(-2))= (5,3,1)\end{array}}$