Question

Quanto é (x-5) (x+5) +5 = x ?
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Answer 1

( x-5).( x+5) +5 = x

x² +5x -5x -25 +5 = x

x² -x -20 = 0


Soma = -b/a = -(-1)/1 = 1

Produto = c/a = -20/1 = -20


Agora precisamos achar dois números cuja soma seja 1 e o produto -20, e são eles:


S = { -4, 5}


Dúvidas só perguntar!

Answer 2

$(x-5).(x+5) +5 = x\\\\\\x~.~x~+~5x~-~5x~-~5~.~5~+~5~=~x\\\\\\x^2-25+5~=~x\\\\\\\boxed{x^2-x-20~=~0}~~\rightarrow~~Aplicando~Bhaskara\\\\\\\Delta~=~(-1)^2-4.1.(-20)~=~1+80~=~\boxed{81}\\\\\\x'~=~\frac{1+\sqrt{81}}{2~.~1}~=~\frac{1+9}{2}~=~\frac{10}{2}~=~\boxed{5}\\\\\\x''~=~\frac{1-\sqrt{81}}{2~.~1}~=~\frac{1-9}{2}~=~\frac{-8}{2}~=~\boxed{-4}$