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Find the non-extraneous solutions of the square root of the quantity x plus 6 minus 5 equals quantity x plus 1.

x = −2
x = −6 and x = −5
x = −6 and x = −2
x = 2

2 Answers

2 votes

Answer:

x = −6 and x = −7

5 votes
The radical equation is
√(x+6)-5=x+1.


i) We first isolate the square root, adding 5 to both sides of the equation:


√(x+6)=x+6.

ii) Here let's substitute x+6 with t. Doing so we have:


√(t)=t.

Squaring both sides, we get:


t=t^2

iii) Collecting the variables on the same side, and factorizing t we have:


t(t-1)=0, which yields

t=0 or t=1.

Now we solve for x in x+6=t:

x+6=0 ⇒x=-6 and x+6=1⇒x=-5.


iv) Now we check these values in the original equation
√(x+6)=x+6 :

a)
√(-6+6)=-6+6. ⇒ 0=0 ; Correct.


b)
√(-5+6)=-5+6. ⇒ 1=1 ; Correct.



Answer: x = −6 and x = −5
User Rajenpandit
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