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AP EAMCET202022 Sep 2020Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

The minimum and maximum values of (x+ 3 )+2 2 (x+ 3 ) are respectively

Options

  1. A-(2 3 -1) and 2 3 -1
  2. B-(1+2 2 ) and 1+2 2
  3. C-3 and 3
  4. D-2 and 2

Correct answer

C. -3 and 3

Step-by-step solution

Let aligned f(x)= & (x+ 3 )+2 2 (x+ 3 ) = & ( x 3 - x 3 ) & +2 2 ( x 3 + x 3 ) aligned aligned &= ( x 1 2 - x 3 2 ) &+2 2 ( x 1 2 + x 3 2 ) &= x 2 - 3 x 2 + 2 x+ 6 x & f(x)= x ( 1 2 + 6 )+ x ( 2 - 3 2 ) & a= 1 2 + 6 and b= 2 - 3 2 & a^2+b^2 = ( 1 2 + 6 )^2+ ( 2 - 3 2 )^2 = 9 & a^2+b^2 = 3 aligned Maximum value of f(x)= a^2+b^2 =3 Minimum value of f(x)=- a^2+b^2 =-3 Hence, option (3) is correct.

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