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CBSE Class 12-science Answered

If a≤0 then roots of x^2−2a|x−a|−3a^2=0 is
Asked by bjayanta | 24 Mar, 2019, 09:03: PM
answered-by-expert Expert Answer
I t space i s space g i v e n space t h a t space a less or equal than 0 space rightwards double arrow space minus a greater or equal than 0 N o w comma space vertical line x minus a vertical line equals x minus a space i f space x greater or equal than a space space....... space left parenthesis I right parenthesis vertical line x minus a vertical line equals a minus x space i f space x less than a space...... space left parenthesis I I right parenthesis U sin g space c o n d i t i o n space left parenthesis I right parenthesis comma space w e space h a v e x squared minus 2 a vertical line x minus a vertical line minus 3 a squared equals 0 rightwards double arrow x squared minus 2 a left parenthesis x minus a right parenthesis minus 3 a squared equals 0 rightwards double arrow x squared minus 2 a x plus 2 a squared minus 3 a squared equals 0 rightwards double arrow x squared minus 2 a x minus a squared equals 0 rightwards double arrow x squared minus 2 a x plus a squared equals 2 a squared rightwards double arrow left parenthesis x minus a right parenthesis squared equals 2 a squared rightwards double arrow x minus a equals plus-or-minus square root of 2 a rightwards double arrow x equals a left parenthesis 1 plus-or-minus square root of 2 right parenthesis B u t space x greater or equal than a space a n d space i f space x equals a left parenthesis 1 plus square root of 2 right parenthesis space rightwards double arrow x less than a space sin c e space a less or equal than 0 S o comma space x equals a left parenthesis 1 plus square root of 2 right parenthesis space i s space n o t space p o s s i b l e T h u s comma space x equals a left parenthesis 1 minus square root of 2 right parenthesis space..... space left parenthesis i right parenthesis A c c o r d i n g space t o space c o n d i t i o n space left parenthesis I I right parenthesis comma space w e space h a v e x squared minus 2 a vertical line x minus a vertical line minus 3 a squared equals 0 rightwards double arrow x squared minus 2 a left parenthesis a minus x right parenthesis minus 3 a squared equals 0 rightwards double arrow x squared minus 2 a squared plus 2 a x minus 3 a squared equals 0 rightwards double arrow x squared minus 2 a x minus 5 a squared equals 0 rightwards double arrow x squared minus 2 a x plus a squared equals 6 a squared rightwards double arrow left parenthesis x minus a right parenthesis squared equals 6 a squared rightwards double arrow x minus a equals plus-or-minus square root of 6 a rightwards double arrow x equals a left parenthesis 1 plus-or-minus square root of 6 right parenthesis N o w comma space x less than a space a n d space i f space x equals a left parenthesis 1 minus square root of 6 right parenthesis space rightwards double arrow space x greater than a space sin c e space a less or equal than 0 S o comma space x equals a left parenthesis 1 minus square root of 6 right parenthesis space i s space n o t space p o s s i b l e T h u s comma space x equals a left parenthesis 1 plus square root of 6 right parenthesis space..... space left parenthesis i i right parenthesis H e n c e comma space x equals a left parenthesis 1 minus square root of 2 right parenthesis comma space a left parenthesis 1 plus square root of 6 right parenthesis
Answered by Renu Varma | 25 Mar, 2019, 10:07: AM

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