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AP EAMCET202315 May 2023Evening ShiftMathematicsTrigonometric Ratios & IdentitiesActual

aligned & If [1- ( 2 + )+ ( 3 2 + ) ]^2+ & [1- ( 3 2 - )- ( 3 2 + ) ]^2=a+b ^2 ( 4 + ) aligned then a^2+b^2=

Options

  1. A20
  2. B52
  3. C40
  4. D32

Correct answer

B. 52

Step-by-step solution

aligned & Since [1- ( 2 + )+ ( 3 2 + ) ]^2 & + [1- ( 3 2 - )- ( 3 2 + ) ]^2 & =a+b ^2 ( 4 + ) & (1+ - )^2+(1+ - )^2 & =a+b ^2 ( 4 + ) & 1+ ^2 + ^2 +2 -2 -2 & +1+ ^2 + ^2 +2 -2 -2 & =a+b ^2 ( 4 + ) & 4-4 =a+b ( ( 4 ) + 4 )^2 & 4-4 =a+ b 2 ( + )^2 & 4-4 =a+ b 2 (1+2 ) & 4-4 =a+ b 2 +b & b=-4, a+ b 2 =4 a=4+2=6 & aligned Now, a^2+b^2=16+36=52

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