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AP EAMCET2010MathematicsFunctions

For x R , the least value of x^2-6 x+5 x^2+2 x+1 is

Options

  1. A-1
  2. B- 1 2
  3. C- 1 4
  4. D- 1 3

Correct answer

D. - 1 3

Step-by-step solution

Let f(x)= x^2-6 x+5 x^2+2 x+1 for x R Let y= x^2-6 x+5 x^2+2 x+1 y x^2+2 y x+y=x^2-6 x+5(y-1) x^2+(2 y+6) x+(y-5)=0x= -2(y+3)+ 4(y+3)^2-4(y-1)(y-5) 2 (y-1) Since, x is real. Then, its discriminant should be 0 . 4(y+3)^2-4(y-1)(y-5) 0 (y+3)^2-(y-1)(y-5) 0 y^2+9+6 y- (y^2-6 y+5 ) 0 y^2+9+6 y-y^2+6 y-5 0 12 y+4 0 4(3 y+1) 0 y -1 / 3 So, least value of given expression is ( -1 3 ) .

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