How do you solve #sqrt(x-4)+ sqrt( x+1)=5#?

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Answer 1 · 2016-08-24T19:56:08

#x=8#

Lets just try something. You never know, it may work!

The standard move to get rid of square root is to square everything.

Write as :#" "sqrt(x-4)=5-sqrt(x+1)#

Squaring both sides

#x-4=5^2-10sqrt(x+1)+(x+1)#

#x-(x+1)+10sqrt(x+1)=25+4#

#-1+10sqrt(x+1)=29#

#sqrt(x+1)=30/10 = 3#

Square both sides

#x+1=9#

#x=8#

#color(brown)("Sometimes it is a matter of trying something. If that does not work")##color(brown)("then try something else.")#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
check

#color(blue)(sqrt(x-4)+sqrt(x+1)=5)color(green)(" "->" "sqrt(8-4)+sqrt(8+1)=5)#

#=>sqrt(4)+sqrt(9)=5#

#2+3=5 larr" Left hand side=Right hand side so true"#