Question

Which equation results from isolating a radical term and squaring both sides of the equation for the equation sqrt(c-2) - sqrt(c) = 5

A) c-2=25+c

B) c-2=25-c

C) c-2 = 25+c-10sqrt(c)

D) c-2 = 25-c+10sqrt(c)

Answer 1

From the options, I don' t think the correct answer could be found from it. To solve the expression given above, for simplicity in simplifying, we transpose one of the radical term to the right side of the equality. Then, we square both sides of the expression to get rid or lessen the radical signs. We do as follows:

sqrt(c-2) - sqrt(c) = 5
sqrt(c-2) = 5 + sqrt(c) 
(sqrt(c-2))^2 = (5 + sqrt(c) )^2
c-2 = ( 5 + sqrt(c) ) ( 5 + sqrt(c) )
By FOIL method, we simplify the right side of the equation.
c-2 = 25 + 5sqrt(c) + 5sqrt(c) + c
c-2 = 25 + 10sqrt(c) + c

Therefore, the answer should be c-2 = 25 + 10sqrt(c) + c which is not in the choices given above.

Answer 2

Answer:

D) c - 2 = 25 + c + 10√c

Step-by-step explanation:

The given equation is sqrt(c-2) - sqrt(c) = 5

Taking square on both sides, we get

Here we used ( a+ b)^2 = a^2 + b^2 + 2ab formula.

c - 2 = 5^2 + (√c)^2 + 2(5)√c

c - 2 = 25 + c +10√c

Hope this helps!! Have a great day!! ❤