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

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

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

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

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