Question

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+c^3​

Answer 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