Given the equation square root of quantity 3x plus 6 end quantity equals 3, solve for x and identify if it is an extraneous solu

Question

3 years ago

15

tion. 1; solution is extraneous 1; solution is not extraneous 3; solution is extraneous 3; solution is not extraneous

1 answer:

Novay_Z [31] · Answer 1 · 2022-04-25T00:43:12+03:00

Solution is not extraneous, x=1 is correct answer

Step-by-step explanation:

We need to solve the equation $\sqrt{3x+6}=3$ and find value of x.

Solving:

$\sqrt{3x+6}=3\\Taking\,\,square\,\,on\,\,both\,\,sides\\(\sqrt{3x+6})^2=(3)^2\\3x+6=9\\Simplifying:\\3x=9-6\\3x=3\\x=3/3\\x=1$

So. Value of x = 1

Now checking if solution is extraneous or not

Solution is extraneous if value of x doesn't satisfy the given equation.

Checking: putting x=1 in the equation $\sqrt{3x+6}=3$

$\sqrt{3x+6}=3\\\sqrt{3(1)+6}=3\\\sqrt{9}=3\\ 3=3$

Since x=1, verifies the given equation so, x=1 is not extraneous solution

Solution is not extraneous, x=1 is correct answer

Keywords: Solving equations and finding extraneous roots

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