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[tex] \rm \orange{ \mathbb Challenge}[/tex] Solve the given question to be a genius. [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt} [/tex] Answer only if u know the answer [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large{\frak{ \pink{Que}{sti} \purple{on - 1 }}}[/tex] [tex] \rm \large \pink{\textit{ \sf{Find \: the \: sum - } }} \\ \large \red{\sf{ \mapsto100 + 200 + 300.... + 10000 }}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large{\frak{ \pink{Que}{sti} \purple{on - 2}}}[/tex] [tex]\rm\pink{\large{\sf{ \mapsto Sum \: of \: 2 \: consecutive }}} \\ {\large{\sf{square \: numbers \: is \: 21.}} }\\ \large \red{\sf{Find \: the \: smallest \: number.}}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large \orange{\bf{No \: Spam }}[/tex] [tex]\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt}[/tex] [tex]\large \fcolorbox{green}{gray}{\tt{ s}}[/tex] [tex]​\blue{ \rule{18mm}{3.5pt}} \red{ \rule18mm3.5pt} \gray{ \rule18mm3.5pt} [/tex] ​

Respuesta :

#1

100+200+300..10000

  • a=100
  • l=10000
  • n=10000/100=100

Now

[tex]\\ \rm\Rrightarrow S_{100}=\dfrac{100}{2}(100+10000)=50(10100)=505000[/tex]

#2

  • Numbers be x and x+1

[tex]\\ \rm\Rrightarrow x^2+(x+1)^2=21[/tex]

[tex]\\ \rm\Rrightarrow x^2+x^2+2x+1=21[/tex]

[tex]\\ \rm\Rrightarrow 2x^2+2x=20[/tex]

[tex]\\ \rm\Rrightarrow x^2+x-10=0[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{1-40}}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{-39}}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm \sqrt{39}i}{2}[/tex]

  • No real solutions

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