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Question

Solve:

(i)x42x23=0 (ii) x410x2+9=0

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Solution

left parenthesis i right parenthesis space x to the power of 4 space � space 2 x squared space � space 3 space equals 0 space x to the power of 4 minus 3 x squared plus x squared minus 3 equals 0 x squared left parenthesis x squared minus 3 right parenthesis plus 1 left parenthesis x squared minus 3 right parenthesis equals 0 left parenthesis x squared minus 3 right parenthesis left parenthesis x squared plus 1 right parenthesis equals 0 x squared minus 3 equals 0 space space space space o r space space space x squared plus 1 equals 0 x equals plus-or-minus square root of 3 space space space space space space o r space space x squared equals negative 1 space left parenthesis r e j e c t right parenthesis left parenthesis i i right parenthesis space x to the power of 4 space end exponent � space 10 x to the power of 2 space end exponent plus 9 space equals 0 x to the power of 4 minus 9 x squared minus x squared plus 9 equals 0 x squared left parenthesis x squared minus 9 right parenthesis minus 1 left parenthesis x squared minus 9 right parenthesis left parenthesis x squared minus 9 right parenthesis left parenthesis x squared minus 1 right parenthesis equals 0 x squared minus 9 equals 0 space space space space space o r space space space space x squared minus 1 equals 0 x equals plus-or-minus 3 space space space space space space space space space o r space space space space space x equals 1

Here, x=-1 will also be a solution.


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