absolute value equation?

Question

solve the equation... show work please!!
thanks

x+1 -2sqrt(x+11)=0

sorry guys i mean square root equation!!

Answer 1

This is not really an absolute value equation but one involving a square root instead. First step is to get the expression involving the square root one one side of the equation. In this example, that is most easily accomplished by adding 2√(x + 11) to both sides, giving

x + 1 = 2√(x + 11)

We can divide the 2 to remove it from the side with the radical, but it isn't really necessary. The main idea is to have a single term on the right so that when we multiply both sides by themselves, i.e., square them, the square root disappears. Once we square both sides, we get

(x + 1)² = 4(x + 11)
x² + 2x + 1 = 4x + 44

We now traded in our radical for a polynomial equation that we can solve like any other polynomial equation. That is, move everything to one side and try to factor or use the quadratic equation or whatever:

x² - 2x - 43 = 0

This example won't factor, so we must use the quadratic equation or complete the square. This gives

x = {2 ± √[(-2)² - 4(1)(-43)]} / 2
= 1 ± 2√11

However, these two solutions, 1 + 2√11 and 1 - 2√11, are only solution candidates. We must still try each in the original equation to see if it fits.

Try 1 + 2√11 first:
1 + 2√11 + 1 - 2√[(1 + 2√11 + 11)] =? 0
2 + 2√11 - 2√(1 + √11)² =? 0
2 + 2√11 - 2|1 + √11| =? 0
2(1 + √11 - (1 + √11) =? 0
2(1 + √11 - 1 - √11) =? 0
2(0) = 0, so that solution works.

Now let's try 1 - 2√11:
1 - 2√11 + 1 - 2√[1 - 2√11 + 11] =? 0
2 - 2√11 - 2√[1 - 2√11 + 11] =? 0
2 - 2√11 - 2√(1 - √11)² =? 0
2 - 2√11 - 2|1 - √11| =? 0
2 - 2√11 - 2(√11 - 1) =? 0
2 - 2√11 - 2√11 + 2 =? 0
4 - 4√11 ≠ 0 so we must throw out this "solution." It would have worked if we were allowed to use the negative root of (1 - √11)² but in this problem only the principal root is permitted.

Answer 2

f(x) = x+1 -2sqrt(x+11)=0 => Domain(f)={x > -11}

x+1=2sqrt(x+11) => (x+1)^2=4(x+11) => x^2 -2x -10=0

=> A = (-2)^2 - (4 * 1 * (-10))=44
=>
x1 = 2+sqrt(11)
x2 = 2-sqrt(11)

Answer 3

There's no absolute value here.

x+1 - 2√(x+11) = 0
x + 1 = 2√(x+11)
x² + 2x + 1 = 4(x+11)
x² + 2x + 1 = 4x + 44
x² - 2x + 1 = 44
(x - 1)² = 44
x - 1 = ±2√11
x = 1 ± 2√11
but 1 - 2√11 won't work.

Answer 4

divide the two aspects of the equation by utilising 3. you will get |2x-5|=39/3 it rather is only yet differently of (re)writing the unique equation. next eliminate the abs value indicators. now you have 2 linear equations: 2x-5=39/3 and 2x-5= - 39/3 from right here you ought to get 2 answer. solid success. frequently, while fixing equations attempt to isolate the words containing the variable on one fringe of the equivalent sign and the constants on the different side. bear in mind that to get x by utilising itself you frequently ought to do the opposite operation. as an occasion in case you have something like 3x-5=a million first you ought to upload 5 to the two aspects of the equivalent sign: 3x=6 and then divide by utilising 3 the two aspects to get x=2.