Question

Find x
$\bf \: \sqrt{12 +x} = \sqrt{20 - x}$
​

Answer 1

Step-by-step explanation:

squaring both terms we get

12+x=20-x

so 2x=20-12

2x=8

x=4

Answer 2

$\large \pmb{\sf{Question :}}$

$\sf Find \: x : \sqrt{12 +x} = \sqrt{20 - x}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large \pmb{\sf{Final \: Answer : }}$

$\pink \bigstar \: \color{maroon} \boxed{\sf \color{green} : \leadsto \: x = 4}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large \pmb{\sf{Method \: 1 : }}$

$\sf: \leadsto \sqrt{12 + x} = \sqrt{20 - x}$

$\footnotesize \color{green} \boxed{ \sf{ \color{maroon}{Consider \: a \: number \sqrt{y}, it \: can \: also \: be \: written \: as \: ( y)^{\frac{1}{2}}}}}$

$\sf: \leadsto (12 + x)^{ \frac{1}{2} } = (20 - x)^{ \frac{1}{2} }$

$\sf: \leadsto (12 + x)^{ \cancel\frac{1}{2} } = (20 - x)^{ \cancel\frac{1}{2} }$

$\sf: \leadsto 12 + x = 20 - x \\ \sf: \leadsto x + x = 20 - 12$

$\sf : \leadsto 2x = 8 \\ \sf: \leadsto x = \frac{8}{2}$

$\red \bigstar \boxed{\sf \color{purple} : \leadsto \: x = 4}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\large \pmb{\sf{Method \: 2 : }}$

$\sf: \leadsto \sqrt{12 + x} = \sqrt{20 - x}$

$\footnotesize \color{green} \boxed{ \textsf{ \color{maroon}{Squaring both the sides}}}$

$\sf: \leadsto 12 + x = 20 - x \\ \sf: \leadsto x + x = 20 - 12$

$\sf : \leadsto 2x = 8 \\ \sf: \leadsto x = \frac{8}{2}$

$\red \bigstar \boxed{\sf \color{purple} : \leadsto \: x = 4}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\sf \color{azure}\fcolorbox{pink}{purple}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \#Bebrainly \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\:\: \: \: \: \:}$

━━━━━━━━━━━━━━━━━━━━━━━━━━

$\sf \color{azure}\fcolorbox{pink}{black}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: @Saanvigrover2007 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}$