How do you solve #2sqrt(x+4) -1=x# and find any extraneous solutions?

1 Answer
Tony B
Aug 19, 2016

In support of the answer by Mark E

Explanation:

Read his solution up to the point

Now Simplify:
#x^2 -2x-15 =0#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
With quadratics if you can not spot the factorisation then it is wise to solve using the formula or completing the square.

#color(blue)("Solve by factorizing")#

Notice that the numbers #3xx5=15" and "5-3=2#

The 15 is negative in the given equation so we must have either

#(-3)xx(+5)#

or

#(+3)xx(-5)#

'.....................................................................
The #2x# is negative so the larger number of the subtraction has to be negative. Giving: #3-5#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Thus we have:

#(x-5)(x+3)=0#

Thus #color(green)(x= +5" and "-3)#

Returning to Mark E's solution shows that -3 is not a valid solution
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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