How do we simplify the expression $\left|\left|\sqrt{-x^2}-1\right|-2\right|$?
This is very confusing. Do they cancel out and become just simply $\sqrt{-x^2}-1-2$?
2026-04-04 06:58:55.1775285935
Simplifying $\left|\left|\sqrt{-x^2}-1\right|-2\right|$
152 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRA-PRECALCULUS
- How to show that $k < m_1+2$?
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Finding the value of cot 142.5°
- Why is the following $\frac{3^n}{3^{n+1}}$ equal to $\frac{1}{3}$?
- Extracting the S from formula
- Using trigonometric identities to simply the following expression $\tan\frac{\pi}{5} + 2\tan\frac{2\pi}{5}+ 4\cot\frac{4\pi}{5}=\cot\frac{\pi}{5}$
- Solving an equation involving binomial coefficients
- Is division inherently the last operation when using fraction notation or is the order of operation always PEMDAS?
- How is $\frac{\left(2\left(n+1\right)\right)!}{\left(n+1\right)!}\cdot \frac{n!}{\left(2n\right)!}$ simplified like that?
- How to solve algebraic equation
Related Questions in PROBLEM-SOLVING
- How do you prevent being lead astray when you're working on a problem that takes months/years?
- How to prove the inequality $\frac{1}{n}+\frac{1}{n+1}+\cdots+\frac{1}{2n-1}\geq \log (2)$?
- How to solve higher order polynomial equations?
- Methods in finding invariant subspaces?
- Question about the roots of a complex polynomial
- Using a counting argument to prove some equalities? (Problem Solving)
- (Problem Solving) Proving $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\frac{1}{k+m+1}=\sum_{k=0}^{m}(-1)^k\binom{m}{k}\frac{1}{k+n+1}$
- (Problem Solving) Proving $|x|^p +|y|^p \geq |x+y|^p$
- Each vertex of the square has a value which is randomly chosen from a set.
- Fill in the blanks
Related Questions in ABSOLUTE-VALUE
- To find the Modulus of a complex number
- What does $|a| = |b|$ is equal to?
- Symmetric polynomial written in elementary polynomials
- If $|ax^2+bx+c|\le \frac12$ for all $|x|\le1$, then $|ax^2+bx+c|\le x^2-\frac12$ for all $|x|\ge1$
- Proving that a double integral converges
- Equation system
- If $\sqrt{9−8\cos 40^{\circ}} = a +b\sec 40^{\circ}$, then what is $|a+b|$?
- Proving that inequalities $\|a\|_{\infty} \leq \|a\|_2 \leq \sqrt{n} \|a\|_{\infty}$ are true and sharp.
- Find a number $M$, such that $|x^3-4x^2+x+1| < M$ for all $1<x<3$
- Absolute Value of a Complex Number Inequality
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Assuming you are working with real numbers only, your expression is only defined if $x = 0$. Following on from that the answer would be $||0 - 1| - 2| = ||-1| - 2| = |1 - 2| = |-1| = 1$.
If we allow x to be complex or imaginary, it gets a bit more, well, complex. Let x be the complex number $a + bi$. Squaring this gives $a^2 + 2abi - b^2$. The negative sign changes this to $b^2 - 2abi - a^2$, and the expression has now become $||ai - b - 1| - 2|$.
If we suppose that the real part of this complex number is 0 (meaning it is a pure imaginary number), then we can get $||-b - 1| - 2|$. The answer would then depend on the value of b. Otherwise, there is no way to simplify this expression; although the absolute value of $a + bi$ is $\sqrt{a^2 + b^2}$ (can you figure out why?) we have flipped the real and imaginary parts, and also have a pesky 1 in the mix.
Note also that the absolute value of the absolute value is indeed the absolute value, but you cannot just "cancel out" the absolute value brackets. As you can see, you must take into account the operations in between; if you had evaluated the brackets as you say the answer would be -3, which is ridiculous, because absolute value gives only positive answers.