Can someone help me solve these equatiions
[SQRT(4 - x)] - [SQRT(x + 6)] = 2
[SQRT(4 - x)] - [SQRT(x + 6)] = 2
√(4-x) = 2 + √(x+6)
square both sides
4-x = 4 + 4√(x+6) + x+6
-2x - 6 = 4√(x+6)
-x - 3 = 2√(x+6)
square again
x^2 + 6x + 9 = 4(x+6)
x^2 + 2x - 15 = 0
(x+5)(x-3) = 0
x = -5 or x = 3
since we squared both answers must be verifies
if x=-5
LS = √9 - √1
= 3 - 1
which is not the RS, so x=-5 does NOT work
if x= 3
LS = √1 - √9
= 1-3
= -2, which is not the RS
So, there is NO solution
if x=
I don't see what -5 does not work. The right side is 2
If you admit negative square roots, +3 works also
"what" should be "why" in my previous answer. I often can't get either the numbers or the words right.
of course you are right, x = -5 works.
don't know what I was thinking!
Yes, I can help you solve this equation.
To solve the equation [SQRT(4 - x)] - [SQRT(x + 6)] = 2, we need to isolate the variable x. Here's how you can do it step-by-step:
Step 1: Start by isolating one of the radicals on one side of the equation. Let's isolate the first radical [SQRT(4 - x)]:
[SQRT(4 - x)] = [SQRT(x + 6)] + 2
Step 2: Square both sides of the equation to eliminate the square root on the left side:
([SQRT(4 - x)])^2 = ([SQRT(x + 6)] + 2)^2
Simplifying the left side of the equation gives us:
4 - x = x + 6 + 4[SQRT(x + 6)] + 4
Step 3: Combine like terms on the right side of the equation:
4 - x = x + 10 + 4[SQRT(x + 6)]
Step 4: Move all terms involving x to one side of the equation:
2x = 4 - 10 - 4[SQRT(x + 6)]
Simplifying the equation further:
2x = -6 - 4[SQRT(x + 6)]
Step 5: Divide both sides of the equation by 2:
x = [-6 - 4[SQRT(x + 6)]] / 2
That is the solution to the equation. Keep in mind that this is an implicit equation that cannot be easily solved algebraically. To find an approximate solution, you can use numerical methods such as graphing, iteration, or a solver tool.