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

Step-by-step solution

This is possible only when aligned & a+b-5=0 ...(i) & b+2 c+3=0 ...(ii) & c+3 a-10=0 ...(iii) aligned On solving, we get aligned & a=4, b=1, c=-2 & a^3+b^3+c^3=57 aligned