Question

√(X+23)+√(X-12)=7
Why X is 13?
Show Steps
please help!

Answer 1

\[\sqrt{x+23}+\sqrt{x-12}=7~~...(1)\]
\[\left( x+23 \right)-\left( x-12 \right)=x+23-x+12=35\]
\[\frac{ \left( x+23 \right)-\left( x-12 \right) }{ \sqrt{x+23}+\sqrt{x-12} }=\frac{ \left( \sqrt{x+23} \right)^2-\left( \sqrt{x-12} \right)^2 }{\sqrt{x+23}+\sqrt{x-12} }=\frac{ 35 }{7 }=5\]
\[\frac{ \left( \sqrt{x+23}+\sqrt{x-12} \right)\left( \sqrt{x+23}-\sqrt{x-12} \right) }{( \sqrt{x+23}+\sqrt{x-12}) }=5\]
\[\sqrt{x+23}-\sqrt{x-12}=5 ~~...(2)\]
adding (1) and (2)
\[2\sqrt{x+23}=7+5=12,\sqrt{x+23}=6\]
squaring both sides
x+23=36
x=?

Answer 2

thanks alot

Answer 3

yw