Question

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

Answer 1

#1

100+200+300..10000

• a=100
• l=10000
• n=10000/100=100

Now

`\\ \rm\Rrightarrow S_(100)=(100)/(2)(100+10000)=50(10100)=505000`

#2

• Numbers be x and x+1

`\\ \rm\Rrightarrow x^2+(x+1)^2=21`

`\\ \rm\Rrightarrow x^2+x^2+2x+1=21`

`\\ \rm\Rrightarrow 2x^2+2x=20`

`\\ \rm\Rrightarrow x^2+x-10=0`

`\\ \rm\Rrightarrow x=(-1\pm√(1-40))/(2)`

`\\ \rm\Rrightarrow x=(-1\pm√(-39))/(2)`

`\\ \rm\Rrightarrow x=(-1\pm √(39)i)/(2)`

• No real solutions