If 2s = a + b + c, then the value of s(s - c) + (s - a) (s - b)

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 Multiple Choice QuestionsMultiple Choice Questions

61.

If p + m = 6 and p3 + m3 = 72, then the value of pm is

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  • 12

  • 9

  • 9

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62.

If fraction numerator 2 straight p over denominator straight p to the power of straight r minus 2 straight p plus 1 end fraction space equals space 1 fourth comma then the value of open parentheses straight p plus 1 over straight p close parentheses is

  • 7

  • 2 over 5
  • 1

  • 1

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63.

If 2s = a + b + c, then the value of s(s - c) + (s - a) (s - b) is

  • ab

  • abc

  • 0

  • 0


A.

ab

2s = a + b + c
therefore space space straight s left parenthesis straight s minus straight c right parenthesis space equals space open parentheses fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction close parentheses space open parentheses fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction minus straight c close parentheses
space space space space space space equals space fraction numerator left parenthesis straight a plus straight b plus straight c right parenthesis space left parenthesis straight a plus straight b minus straight c right parenthesis over denominator 4 end fraction
Again, (s - a) (s - b)
      equals space 1 fourth left parenthesis 2 straight s minus 2 straight a right parenthesis thin space left parenthesis 2 straight s minus 2 straight b right parenthesis
equals space 1 fourth left parenthesis straight a plus straight b plus straight c minus 2 straight a right parenthesis thin space left parenthesis straight a plus straight b plus straight c minus 2 straight b right parenthesis
equals space 1 fourth left parenthesis straight b plus straight c minus straight a right parenthesis thin space left parenthesis straight a plus straight c minus straight b right parenthesis

therefore space space straight s left parenthesis straight s minus straight c right parenthesis space plus space left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight b right parenthesis
 equals space 1 fourth left square bracket left parenthesis straight a plus straight b plus straight c right parenthesis space left parenthesis straight a plus straight b minus straight c right parenthesis space plus space left parenthesis straight b plus straight c minus straight a right parenthesis thin space left parenthesis straight a plus straight c minus straight b right parenthesis right square bracket
equals space 1 fourth left square bracket left parenthesis straight a plus straight b right parenthesis squared minus straight c squared plus space ab space plus space ac minus straight a squared space plus space bc space plus space straight c squared minus ac minus straight b squared minus bc plus ab right square bracket

equals space 1 fourth left square bracket straight a squared plus straight b squared plus 2 ab minus straight c squared plus ab plus ac minus straight a squared plus bc plus straight c squared minus ac minus straight b squared minus bc plus ab right parenthesis
equals space 1 fourth space cross times space 4 ab space equals space ab

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64.

If straight a squared plus straight b squared plus straight c squared space equals space ab space plus bc plus space ac then the value of fraction numerator straight a plus straight c over denominator straight b end fraction is

  • 0

  • 2

  • 1

  • 1

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65.

If ab + bc + ca = 0, then the value of open parentheses fraction numerator 1 over denominator straight a squared minus bc end fraction space plus space fraction numerator 1 over denominator straight b squared minus ca end fraction plus fraction numerator 1 over denominator straight c squared minus ab end fraction close parentheses is

  • 0

  • 1

  • 3

  • 3

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66.

If left parenthesis 2 plus square root of 3 right parenthesis straight a space equals space left parenthesis 2 minus square root of 3 right parenthesis straight b space equals space 1 then the value of 1 over straight a plus 1 over straight b is

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  • 2 square root of 3
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67.

If 3 straight x plus 3 over straight x space equals space 1, then straight x cubed plus 1 over straight x cubed plus 1 is

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  • 1 over 27
  • 5 over 27
  • 5 over 27
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68.

The factors of  are

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69.

If 4x + 5y = 83 and 3x : 2y =  21 : 22, then (y - x) is

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  • 11

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70.

If x = 11, then the value of 
  is

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  • 20

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