Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Ernesto solves the equation below by first squaring both sides of the equation. What extraneous solution does Ernesto obtain?

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Precalculusright chevron icon
Absolute values of complex numbersright chevron icon

Full solution

Q. Ernesto solves the equation below by first squaring both sides of the equation. What extraneous solution does Ernesto obtain?
  1. Square Both Sides: Ernesto starts with the equation: x=x−2\sqrt{x} = x - 2. To eliminate the square root, he squares both sides: (x)2=(x−2)2(\sqrt{x})^2 = (x - 2)^2
  2. Simplify Equation: Simplify both sides: x=x2−4x+4x = x^2 - 4x + 4
  3. Rearrange to Zero: Rearrange the equation to set it to zero: x2−5x+4=0x^2 - 5x + 4 = 0
  4. Factorize Quadratic: Factorize the quadratic equation: (x−4)(x−1)=0(x-4)(x-1) = 0
  5. Solve for x: Solve for x: x=4x = 4 or x=1x = 1
  6. Check Solutions: Check each solution in the original equation x=x−2\sqrt{x} = x - 2. For x=4x = 4: 4=4−2\sqrt{4} = 4 - 2, 2=22 = 2, which is true. For x=1x = 1: 1=1−2\sqrt{1} = 1 - 2, 1=−11 = -1, which is false

More problems from Absolute values of complex numbers

Question
Simplify.\newline8i+6i8i + 6i\newline\newlineWrite your answer in the form a+bia + bi.\newline‾\underline{\hspace{1cm}}\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Find the complex conjugate of the given number.\newline4+10i4 + 10i\newline\newlineWrite your answer in the form a+bia + bi.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Simplify.\newline−4i−9i\frac{{-4i}}{{-9i}}\newline\newlineWrite your answer in the form a+bia + bi. Reduce all fractions.\newline_____\_\_\_\_\_\newline
Get tutor helpright-arrow

Posted 2 months ago

Question
Combine the like terms to create an equivalent expression.\newline7k−k+19=07k-k+19=\boxed{\phantom{0}}
Get tutor helpright-arrow

Posted 4 months ago

Question
Apply the distributive property to factor out the greatest common factor.\newline9+12n= 9+12 n=
Get tutor helpright-arrow

Posted 1 month ago

Question
Solve the equation.\newline12=n−9n=□ \begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}
Get tutor helpright-arrow

Posted 4 months ago

Question
What is the amplitude of y=−sin⁡(8x−3)+5 y=-\sin (8 x-3)+5 ?\newlineunits
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the period of\newliney=4sin⁡(−2x+7)−1 ?  y=4 \sin (-2 x+7)-1 \text { ? } \newlineGive an exact value.\newlineunits
Get tutor helpright-arrow

Posted 2 months ago

Question
3⋅(3+20i)= 3 \cdot(3+20 i)= \newlineYour answer should be a complex number in the form a+bi a+b i where a a and b b are real numbers.
Get tutor helpright-arrow

Posted 4 months ago

Question
(35−23i)+(13+25i)= (35-23 i)+(13+25 i)= \newlineExpress your answer in the form (a+bi) (a+b i) .
Get tutor helpright-arrow

Posted 2 months ago

View all (5)