What is the solution to this system of equations?
1 answer:
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The radical equation is 
.
i) We first isolate the square root, adding 5 to both sides of the equation:
ii) Here let's substitute x+6 with t. Doing so we have:
Squaring both sides, we get:
iii) Collecting the variables on the same side, and factorizing t we have:
, 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
:
a)
⇒ 0=0 ; Correct.
b)
⇒ 1=1 ; Correct.
Answer: <span>x = −6 and x = −5 </span>
i) We first isolate the square root, adding 5 to both sides of the equation:
ii) Here let's substitute x+6 with t. Doing so we have:
Squaring both sides, we get:
iii) Collecting the variables on the same side, and factorizing t we have:
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
a)
b)
Answer: <span>x = −6 and x = −5 </span>