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Olympiad workbook
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Olympiad workbook
Subject
IOQM
Chapter
Determinants

Olympiad workbook · IOQM · Determinants

If a, b, c are real numbers and (a+b-5)^2+(b+2 c+3)^2+(c+3...

If a,b,ca, b, c are real numbers and (a+b−5)2+(b+2c+3)2+(c+3a−10)2=0(a+b-5)^2+(b+2 c+3)^2+(c+3 a-10)^2=0 find the integer nearest to a3+b3+c3a^3+b^3+c^3.

Correct answer

57

Step-by-step solution

This is possible only when a+b−5=0...(i)b+2c+3=0...(ii)c+3a−10=0...(iii)\begin{aligned} & a+b-5=0 ...(i)\\ & b+2 c+3=0 ...(ii)\\ & c+3 a-10=0 ...(iii) \end{aligned} On solving, we get a=4,b=1,c=−2a3+b3+c3=57\begin{aligned} & a=4, b=1, c=-2 \\ & a^3+b^3+c^3=57 \end{aligned}
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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… Olympiad workbook Full Determinants list All Olympiad workbook PYQs