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CBSE Class 11-science Answered

Solve for x |x^2-5x+7|-1|=x^2-3x-4. | means modulus
Asked by Moorti | 25 Jun, 2019, 06:11: PM
answered-by-expert Expert Answer
Coefficient of the given quadratic equation is 1 which is greater than 0
Its discriminant = 25-28=-3<0
T h e r e f o r e comma space x squared minus 5 x plus 7 greater or equal than 0 rightwards double arrow open vertical bar vertical line x squared minus 5 x plus 7 vertical line minus 1 close vertical bar equals x squared minus 3 x minus 4 rightwards double arrow open vertical bar x squared minus 5 x plus 7 minus 1 close vertical bar equals x squared minus 3 x minus 4 rightwards double arrow open vertical bar x squared minus 5 x plus 6 close vertical bar equals x squared minus 3 x minus 4 rightwards double arrow open vertical bar left parenthesis x minus 3 right parenthesis left parenthesis x minus 2 right parenthesis close vertical bar equals x squared minus 3 x minus 4 I f space x less than 2 space o r space x greater than 3 comma space t h e n space left parenthesis x minus 3 right parenthesis left parenthesis x minus 2 right parenthesis greater than 0 i f space x element of left parenthesis 2 comma 3 right parenthesis comma space t h e n space left parenthesis x minus 3 right parenthesis left parenthesis x minus 2 right parenthesis less than 0 I f space x less than 2 space o r space x greater than 3 rightwards double arrow x squared minus 5 x plus 6 equals x squared minus 3 x minus 4 rightwards double arrow x equals 5 I f space x element of left parenthesis 2 comma 3 right parenthesis rightwards double arrow negative open parentheses x squared minus 5 x plus 6 close parentheses equals x squared minus 3 x minus 4 rightwards double arrow negative x squared plus 5 x minus 6 equals x squared minus 3 x minus 4 rightwards double arrow 2 x squared minus 8 x plus 2 equals 0 rightwards double arrow x squared minus 4 x plus 1 equals 0 rightwards double arrow x equals fraction numerator 4 plus-or-minus square root of 16 minus 4 end root over denominator 2 end fraction equals 2 plus-or-minus square root of 3 rightwards double arrow x equals 3.73 space o r space 0.2 comma space t h i s space i s space n o t space p o s s i b l e space a s space x element of left parenthesis 2 comma 3 right parenthesis H e n c e comma space x equals 5
Answered by Renu Varma | 27 Jun, 2019, 11:01: AM

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