Check And Help?
1. √x-10+4=0
Answer: x=26
2.√3x+1=7
Answer: x=16
Help With These:
3. √x+6=x
how would you solve this?
I don't get how would It?
4. √x+4 = √x-1+1
it looks similar to problem 2 but it doesn't quite have the same amount of numbers in the same spots..
So I'm stuck on how to solve it.
√(x-10) + 4 = 0
if x=26, you have
√16 + 4 = 0
which is not true.
√n is a positive value, so there is no solution.
Now, √(x-10) - 4 = 0 has solution x=26
√(3x+1) = 7
has the solution x=16 as you say.
√(x+6) = x
square both sides:
x+6 = x^2
now solve as a quadratic
x = -2 or 3
However, √4 = 2, not -2, so -2 is an extraneous solution introduced by squaring. -2+6 = 4 = (-2)^2, but √4 = 2, not -2.
same method here:
x+4 = (x-1) + 2√(x-1) + 1
4 = 2√(x-1)
16 = 4(x-1)
x = 5
check: √(5+4) = √9 = 3 = √(5-1)+1 OK
Sure, I'd be happy to help you with these questions!
For question 3, √x+6 = x, you can solve it by isolating the square root expression on one side of the equation and the variable on the other side. Here's the step-by-step solution:
Step 1: Square both sides of the equation to eliminate the square root: (√x + 6)^2 = x^2
Step 2: Simplify the left side of the equation by expanding the square: (x + 6)^2 = x^2
Step 3: Expand the square on the left side: x^2 + 12x + 36 = x^2
Step 4: Simplify the equation by canceling out x^2 terms: 12x + 36 = 0
Step 5: Subtract 36 from both sides to isolate the variable: 12x = -36
Step 6: Divide both sides by 12 to solve for x: x = -3
Therefore, the solution to the equation √x+6 = x is x = -3.
Now, let's move on to question 4, √x+4 = √x-1+1. This equation does look similar to problem 2, but the expressions on each side of the equation are slightly different. Here's how you can solve it:
Step 1: Squaring both sides of the equation: (√x + 4)^2 = (√x - 1 + 1)^2
Step 2: Expanding the squares on both sides: x + 8√x + 16 = (x - 1 + 1)^2
Step 3: Simplifying the right side: x + 8√x + 16 = (x)^2
Step 4: Expanding the square on the right side: x + 8√x + 16 = x^2
Step 5: Moving all terms to one side of the equation: x^2 - x - 8√x - 16 = 0
At this point, we have a quadratic equation in terms of x and √x, which makes it more challenging to solve. However, we can still attempt to isolate one of the variables and find a solution. Keep in mind that there may be additional steps required that are not shown here.
I hope this helps you understand how to approach and solve these equations step-by-step. If you have any further questions or need additional explanations, please let me know!