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(2x-3)^2 - |2x-3| -2 =0
Asked by mehraakshita419 | 23 Jul, 2022, 08:44: AM
answered-by-expert Expert Answer
When 2x - 3 > 0 i.e. x > 3/2
Therefore, (2x-3)^2 - (2x - 3) - 2 =0
i.e. (2x-3)^2 - (2x-3) -2 =0
rightwards double arrow 4 x squared minus 12 x plus 9 minus 2 x plus 3 minus 2 equals 0
rightwards double arrow 4 x squared minus 14 x plus 10 equals 0
rightwards double arrow 2 x squared minus 7 x plus 5 equals 0
rightwards double arrow left parenthesis 2 x minus 5 right parenthesis left parenthesis x minus 1 right parenthesis equals 0
rightwards double arrow x equals 5 over 2 space space o r space space x equals 1
rightwards double arrow straight x equals 5 over 2 comma space since space straight x greater than 3 over 2

W h e n space 2 x minus 3 less than 0 space space i. e. space x less than 3 over 2
rightwards double arrow 4 x squared minus 12 x plus 9 plus 2 x minus 3 minus 2 equals 0
rightwards double arrow 4 x squared minus 10 x plus 4 equals 0
rightwards double arrow 2 x squared minus 5 x plus 2 equals 0
rightwards double arrow left parenthesis 2 x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis equals 0
rightwards double arrow x equals 1 half space space o r space space x equals 2
rightwards double arrow straight x equals 1 half comma space since space straight x less than 3 over 2
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