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

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Answer 1 · 2016-07-26T15:42:15

$v=+4$

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:

$(v-4)^2=0$

$=>v=+4$

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