Solving Radical Equations x−7=x−5

estadsocm3

estadsocm3

Answered

2022-01-21

Solving Radical Equations
x7=x5

Answer & Explanation

sainareon2

sainareon2

Expert

2022-01-22Added 10 answers

Step 1
We can avoid squaring both sides.
Let
x5=u2,
where
u0
Then
x5=u
Also,
x=u2+5
so
x7=u22
Thus our equation can be rewritten as
u22=u
or equivalently
u2u2=0
But
u2u2=(u2)(u+1)
Thus the solutions of
u2u2=0
are
u=2
and  u=1
Since u0, we reject the solution u=1
We conclude that u=2, and therefore x=u2+5=9.

Kudusind

Kudusind

Expert

2022-01-23Added 11 answers

Step 1
x7=x5
(x7)2=x52
(x7)2=x5
(x7)(x7)=x5
x27x7x+49=x5
x215x+54=0
(x9)(x6)=0
x9=0 or x6=0
x=9 or x=6
Now check for extraneous solutions
RizerMix

RizerMix

Expert

2022-01-27Added 437 answers

Step 1 (x7)=x5 Check the domain first x50x70 x7 (x7)2=x52 (x7)2=x5 (x7)(x7)=x5 x27x7x+49=x5 x215x+54=0 (x9)(x6)=0 x9=0 or x6=0 x=9 or x=6 checking the domain x=6 is an extraneous root. x=9

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