MHB How do I rewrite expressions using absolute value?

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Absolute
AI Thread Summary
The absolute value definition states that |x| equals x for non-negative x and -x for negative x. An example provided involves rewriting the expression |1 - sqrt{2}| + 1. Since 1 - sqrt{2} is negative, it is rewritten as -(1 - sqrt{2}) + 1. This simplifies to -1 + sqrt{2} + 1, resulting in sqrt{2}. The final answer is confirmed as correct.
mathdad
Messages
1,280
Reaction score
0
The definition of absolute value states the following:

| x | = x when x is > or = 0

| x | = -x when x < 0

I can use the above definition to rewrite expressions that do not contain absolute values.

| 1 - sqrt{2} | + 1

The value 1 - sqrt{2} is less than 0.

So, we have -(1 - sqrt{2}) + 1.

-1 + sqrt{2} + 1

Answer: sqrt{2}

Correct?
 
Mathematics news on Phys.org
Yes, this is correct.
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Thread 'Video on imaginary numbers and some queries'
Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
Thread 'Unit Circle Double Angle Derivations'
Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

Similar threads

Back
Top