Grade 11Algebra
Please solve Kar dena is problem ko iitians........ which is based on modulus
Please solve Kar dena is problem ko iitians........ which is based on modulus
1 Answer
Ashesh
Approved Tutor Answer8 Years ago$\left|x^2-1\right|+x+1=0$|x2−1|+x+1=0
- $\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}$Subtract x from both sides$\left|x^2-1\right|+x+1-x=0-x$|x2−1|+x+1−x=0−x
- $\mathrm{Simplify}$Simplify$\left|x^2-1\right|+1=-x$|x2−1|+1=−x
- $\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}$Subtract 1 from both sides$\left|x^2-1\right|+1-1=-x-1$|x2−1|+1−1=−x−1
- $\mathrm{Simplify}$Simplify$\left|x^2-1\right|=-x-1$|x2−1|=−x−1
- $\mathrm{Test\:each\:absolute\:for\:its\:positive\:and\:negative\:ranges}$Test each absolute for its positive and negative rangesShow Steps$x^2-1\ge\:0\:\mathrm{for}\:x\le\:-1\quad\mathrm{or}\quad\:x\ge\:1,\:\quad\mathrm{therefore\:for}\:x\le\:-1\quad\mathrm{or}\quad\:x\ge\:1\quad\left|x^2-1\right|=x^2-1$x2−1≥ 0 for x≤ −1 or x≥ 1, therefore for x≤ −1 or x≥ 1 |x2−1|=x2−1Show Steps$x^2-1x2−10 for −1x1, therefore for −1x1 |x2−1|=−(x2−1)
- $\mathrm{Evaluate\:the\:expression\:in\:the\:following\:ranges:}$Evaluate the expression in the following ranges:$xx−1, −1≤ x1, x≥ 1
- $\mathrm{For:}\:xFor: x−1$\mathrm{Replace:}\:\left|x^2-1\right|\:\mathrm{with}\:\left(x^2-1\right)$Replace: |x2−1| with (x2−1)Show Steps$x^2-1+x+1=0\quad:\quad x=0,\:x=-1$x2−1+x+1=0 : x=0, x=−1$x=0,\:x=-1$x=0, x=−1
- $\mathrm{For:}\:-1\le\:xFor: −1≤ x1$\mathrm{Replace:}\:\left|x^2-1\right|\:\mathrm{with}\:-\left(x^2-1\right)$Replace: |x2−1| with −(x2−1)Show Steps$-\left(x^2-1\right)+x+1=0\quad:\quad x=-1,\:x=2$−(x2−1)+x+1=0 : x=−1, x=2$x=-1,\:x=2$x=−1, x=2
- $\mathrm{For:}\:x\ge\:1$For: x≥ 1$\mathrm{Replace:}\:\left|x^2-1\right|\:\mathrm{with}\:\left(x^2-1\right)$Replace: |x2−1| with (x2−1)Show Steps$x^2-1+x+1=0\quad:\quad x=0,\:x=-1$x2−1+x+1=0 : x=0, x=−1$x=0,\:x=-1$x=0, x=−1
- $\mathrm{Combine\:the\:ranges}$Combine the ranges$\left(x(x−1 and (x=0 or x=−1)) or (−1≤ x1 and (x=−1 or x=2)) or (x≥ 1 and (x=0 or x=−1))
- $x=-1$x=−1
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