Extraneous Solutions
Extraneous solutions, a concept prevalent in algebraic equations and inequalities, introduce a layer of complexity to the problem-solving process. These solutions, while mathematically valid, may not satisfy the original equation and can mislead unwary solvers. Recognizing and comprehending extraneous solutions are crucial for maintaining precision in mathematical reasoning. In this exploration, we delve into the intricacies of extraneous solutions, dissecting their origins and implications within the realm of algebraic problem-solving. Through a concise examination, we aim to unravel the nuanced nature of these solutions, enhancing our understanding of their role in mathematical discourse.
Questions
- How do you solve #\frac { 3} { x + 1} + \frac { 3} { x + 2} + \frac { 3} { x - 1} + \frac { 3} { x - 2} = 0#?
- How can this be solved??? help !!
- What are some examples of extraneous solutions to equations?
- How do you solve #(3x-4)/(x^2-10x+21)-(x-8)/(x^2-18x+77)=(x-5)/(x^2-14x+33)# and check for extraneous solutions?
- How do you solve #(n+5)/(n+8)=1+6/(n+1)# and check for extraneous solutions?
- The polynomial #8x^3-36x^2+22x+21=0# has roots which form an arithmetic progression. How do you find the roots?
- How do you solve #5-3/(2x-1)=(x-4)/(2x-1)# and check for extraneous solutions?
- Find k such that x+3 is a factor of s(x)=x^3 +kx^2 +kx-15???
- If f(x)=3-2x and g(x)=1/x+5. what is the value of (f/g)(8)?
- IF the equation #(a^2-4a+3)x^2+(a-1)x+(a^2-1)=0# has infinite roots, then the value of #a# is ?
- How do I check for extraneous solutions?
- How do you solve #6/(x+2)+5/(x-2)=20/(x^2-4)# and check for extraneous solutions?
- Given f(x)=2x and g(x)=x^2, evaluate : 1. f[g(3)] 2. g[f(3)] How do I solve 1. and 2. ?
- How do extraneous solutions arise from radical equations?
- How to decompose into partial fractions: #(3x)/((x+3)sqrt (x^2+1))# ?
- How do extraneous solutions arise?
- What are common mistakes students make with respect to extraneous solutions?
- How do I solve for x in 3^(2x+2)+8*3^(x)-1=0 ?
- Solve the equation #3^(2x) -9(3^(2x))=8#?
- How do you solve #1=1/(1-a)+a/(a-1)#?