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solve-x-2-4x-5-7-




Question Number 24662 by NECx last updated on 24/Nov/17
solve ∣x^2 −4x−5∣=7
$$\boldsymbol{{solve}}\:\mid{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}\mid=\mathrm{7} \\ $$$$ \\ $$
Answered by mrW1 last updated on 24/Nov/17
x^2 −4x−5=±7  x^2 −4x+4=9±7  (x−2)^2 =9±7  (x−2)^2 =16    ...(i)  x−2=±4  x=2±4=−2, 6    (x−2)^2 =2    ...(ii)  x−2=±(√2)  x=2±(√2)=2+(√2), 2−(√2)
$${x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}=\pm\mathrm{7} \\ $$$${x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{4}=\mathrm{9}\pm\mathrm{7} \\ $$$$\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{9}\pm\mathrm{7} \\ $$$$\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{16}\:\:\:\:…\left({i}\right) \\ $$$${x}−\mathrm{2}=\pm\mathrm{4} \\ $$$${x}=\mathrm{2}\pm\mathrm{4}=−\mathrm{2},\:\mathrm{6} \\ $$$$ \\ $$$$\left({x}−\mathrm{2}\right)^{\mathrm{2}} =\mathrm{2}\:\:\:\:…\left({ii}\right) \\ $$$${x}−\mathrm{2}=\pm\sqrt{\mathrm{2}} \\ $$$${x}=\mathrm{2}\pm\sqrt{\mathrm{2}}=\mathrm{2}+\sqrt{\mathrm{2}},\:\mathrm{2}−\sqrt{\mathrm{2}} \\ $$
Commented by NECx last updated on 24/Nov/17
thank you very much sir.
$${thank}\:{you}\:{very}\:{much}\:{sir}. \\ $$
Commented by NECx last updated on 24/Nov/17
can the answers from an absolute  value also be represented in  intervals,if so please how can the  answer be represented.
$${can}\:{the}\:{answers}\:{from}\:{an}\:{absolute} \\ $$$${value}\:{also}\:{be}\:{represented}\:{in} \\ $$$${intervals},{if}\:{so}\:{please}\:{how}\:{can}\:{the} \\ $$$${answer}\:{be}\:{represented}. \\ $$
Commented by Joel578 last updated on 24/Nov/17
I think it couldn′t
$$\mathrm{I}\:\mathrm{think}\:\mathrm{it}\:\mathrm{couldn}'\mathrm{t} \\ $$

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