Help with these two questions

-Whiplash-

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Jan 22, 2014
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Hello, I was working on a math assignment and I got stuck on these two questions:

7. Solve: Sqrt(2x+25) - 2 Sqrt(x+4) = 1

I know the answer is 0 but I don't know how to remove the Square roots without ending up that x somehow equals 20.

8. Solve:
{ x +2y =16
{
{ Sqrt(x-2) = y-3

What is this question asking me to do? what does the long { containing two terms mean? Does it mean that they want me to find out when (Sqrt(x-2) = y-3=x +2y =16)?
 
Hello, I was working on a math assignment and I got stuck on these two questions:

7. Solve: Sqrt(2x+25) - 2 Sqrt(x+4) = 1

I know the answer is 0 but I don't know how to remove the Square roots without ending up that x somehow equals 20.

x = 12 is also an answer of the resulting quadratic equation.

However, that is an extraneous solution - generated due to squaring the problem.


Notice, introduction of x=12 in the left-hand-side (LHS) produces -1 for RHS.

8. Solve:
{ x +2y =16
{
{ Sqrt(x-2) = y-3
squaring)
What is this question asking me to do? what does the long { containing two terms mean? Does it mean that they want me to find out when (Sqrt(x-2) = y-3=x +2y =16)?
.

For #8, you have 2 equations and 2 unknowns. Convert to (by squaring),

x + 2y = 16 and
x -2 = y2 - 6y + 9

then

(16 - 2y) - 2 = y2 - 6y + 9

y2 - 4y - 5 = 0

Now continue.....
 
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