CBSE Class 11-science Answered
|x|³-7|x|+6=0 pls solve with modulus
Asked by sohammukherjee0007 | 04 Oct, 2023, 11:01: AM
Given equation is
![begin mathsize 14px style open vertical bar x close vertical bar cubed space minus space 7 space open vertical bar x close vertical bar space plus space 6 space equals space 0 end style](https://images.topperlearning.com/topper/tinymce/cache/099aa2b74d7e46091a1b0b856712a990.png)
Above expression is true when |x| = 1 .
If we divide above expression by ( |x|- 1 ), then we get![begin mathsize 14px style fraction numerator open vertical bar x close vertical bar cubed minus 7 open vertical bar x close vertical bar plus 6 over denominator left parenthesis open vertical bar x close vertical bar minus 1 space right parenthesis end fraction space equals space open vertical bar x close vertical bar squared plus vertical line x vertical line minus 6 end style](https://images.topperlearning.com/topper/tinymce/cache/454b9d090d4237a0de71445c7135f99f.png)
![begin mathsize 14px style fraction numerator open vertical bar x close vertical bar cubed minus 7 open vertical bar x close vertical bar plus 6 over denominator left parenthesis open vertical bar x close vertical bar minus 1 space right parenthesis end fraction space equals space open vertical bar x close vertical bar squared plus vertical line x vertical line minus 6 end style](https://images.topperlearning.com/topper/tinymce/cache/454b9d090d4237a0de71445c7135f99f.png)
The quotient |x|2 +|x| - 6 satisfies the condition " |x|2 +|x| - 6 = 0 " , when |x|=2
Hence |x| = 1 , and |x| = 2 are the solution of eqn. (1)
Answered by Thiyagarajan K | 04 Oct, 2023, 12:54: PM
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