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How do you solve this ? Check for extraneous solutions

How do you solve this ? Check for extraneous solutions-example-1
User Terdon
by
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1 Answer

3 votes

ANSWER


x = 6

Step-by-step explanation

The given equation is


√(3x + 7) = x - 1

We square both sides of the equation to obtain,


(√(3x + 7) ) ^(2) =( x - 1)^(2)

This implies that,


3x + 7 = {x}^(2) - 2x + 1

Rewrite in standard quadratic equation form.


{x}^(2) - 2x - 3x+ 1 - 7 = 0


{x}^(2) -5x - 6= 0

Factor


(x - 6)(x + 1) = 0

This implies that,


x = 6 \: x = - 1

We check for extraneous solution by substituting each x-value into the original equation.

When x=-1,


√(3( - 1)+ 7) = - 1- 1


√(4) = - 2

2=-2....False

Hence x=-1 is an extraneous solution.

When x=6,


√(3( 6)+ 7) = 6- 1


√(25) = 5

5=5 is True.

Hence x=6 is the only solution.

User Vinton
by
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