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AP EAMCET202421 May 2024Morning ShiftMathematicsTrigonometric EquationsActual

If P+Q+R= 4 , then ( 8 -P )+ ( 8 -Q )+ ( 8 -R )=

Options

  1. A4 P 2 Q 2 R 2 - 8
  2. B4 P 2 Q 2 R 2 + 8
  3. C4 P 2 Q 2 R 2 - 8
  4. D4 P 2 Q 2 R 2 + 8

Correct answer

A. 4 P 2 Q 2 R 2 - 8

Step-by-step solution

aligned & Given that P + Q + R = 4 & array l ( 8 - P )+ ( 8 - Q )+ ( 8 - R ) =2 1 2 ( 4 -( P + Q ) ) 1 2 ( Q - P )+ ( 8 - R )+ 8 - 8 =2 R 2 1 2 ( Q - P )+2 1 2 ( 4 - R ) R 2 - 8 =2 R 2 1 2 ( Q - P )+2 1 2 ( P + Q ) R 2 - 8 =2 R 2 [ 1 2 ( P - Q )+ 1 2 ( P + Q ) ]- 8 =4 R 2 P 2 Q 2 - 8 array aligned

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