1. If a, b, c are real numbers and
(a + b – 5)2 + (6 + 2c + 3)2 +(c + 3a – 10)2 =0
find the integers nearest to a^3+b^3+

1 thought on “1. If a, b, c are real numbers and<br />(a + b – 5)2 + (6 + 2c + 3)2 +(c + 3a – 10)2 =0<br />find the integers nearest to a^3+b^3+”

1. Question :-

   If a , b and c are real numbers and

   ( a + b – 5 )² + ( 6 + 2c + 3 )² + ( c + 3a – 10 )² = 0

   Find the integer nearest to a³ + b³ + c³.

   Answer :-

   Here, sum of squares is zero. As the squares can never be negative, each of the the numbers should be equal to zero.

   → a + b – 5 = 0 -i

   → 6 + 2c + 3 = 0 -ii

   → c + 3a – 10 = 0 -iii

   From eqaution ii :-

   → 6 + 2c + 3 = 0

   → 2c + 9 = 0

   → 2c = -9

   → c = – 4.5

   Substituting the value in equation iii :-

   → c + 3a – 10 = 0

   → – 4.5 + 3a – 10 = 0

   → 3a – 14.5 = 0

   → 3a = 14.5

   → a = 14.5 / 3

   Subtituting the value in equation i :-

   → a + b – 5 = 0

   → 14.5 / 3 – 5 + b = 0

   → (14.5 – 15) / 3 + b = 0

   → b = 3 / 0.5

   → b = 6

   a³ + b³ + c³ = ( 14.5 / 3 )³ + 6³ + ( – 4.5 )³

   = 112.912 + 216 – 91.125

   = 237.78

   Integer nearest to 237.78 = 238

   Required answer = 238

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