SOLUTION: I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why. (rad of 4-x PLUS the rad of x+6)

Algebra ->  Radicals -> SOLUTION: I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why. (rad of 4-x PLUS the rad of x+6)       Log On


   

Question 849769: I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
(rad of 4-x PLUS the rad of x+6) all equal to 4
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
(rad of 4-x PLUS the rad of x+6) all equal to 4
----------
sqrt(4-x) + sqrt(x+6) = 4
--------
Square both sides to get:
(4-x) + (x+6) + 2sqrt[(4-x)(x+6)] = 16
-----
2sqrt(-x^2-2x+24) = 6
----
sqrt(-x^2-2x+24) = 3
Square both sides to get:
-x^2-2x+24 = 9
---
x^2 + 2x - 15 = 0
----
Factor:
(x+5)(x-3) = 0
x = 3 or x = -5
----
Neither is extraneous.
Cheers,
Stan H.
======================

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Description: (rad of 4-x PLUS the rad of x+6) all equal to 4
can best be understood to mean: sqrt%284-x%29%2Bsqrt%28x%2B6%29=4.

When you think you have finished finding the values for x, and you want to know if any is extraneous, you can check how the value works in the ORIGINAL equation.

CHECK -5.
sqrt%284-%28-5%29%29%2Bsqrt%28-5%2B6%29=4?
sqrt%289%29%2Bsqrt%281%29=4
3%2B1=4
TRUE!
x=-5.

CHECK 3.
sqrt%284-3%29%2Bsqrt%283%2B6%29=4?
sqrt%281%29%2Bsqrt%289%29=4
1%2B3=4
TRUE.
x=3.

BOTH solutions work in the original equation.