How do you solve #sqrt(2v-7)=v-3#?

1 Answer
Jul 26, 2016

Answer:

#v=+4#

Explanation:

Roots make life a bit more difficult so lets get rid of it!

Square both sides

#2v-7=(v-3)^2#

#2v-7=(v-3)(v-3)# ......................Equation(1)
,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider #color(blue)((v-3))color(brown)((v-3))#

Multiply everything in the right hand bracket by everything in the left hand bracket.

#color(brown)(color(blue)(v)(v-3)color(blue)(-3)(v-3))#

#=v^2-3v" "-3v+9#

#=v^2-6v+9#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So Equation(1) becomes

#2v-7" "=" "v^2-6v+9#

Add 7 and subtract #2v# from both sides giving:

#0=v^2-8v+16#

Notice that # -4-4=-8" and "(-4)xx(-4)=+16#

Factorising gives:

#(v-4)^2=0#

#=>v=+4#