Question

without actually calculating the cubes,find the value of (_11)^3+5^3+6^3​

Answer 1

We know the corollary: if a+b+c=0 then a3+b3+c3=3abc

Using the above corollary taking a=−10, b=3 and c=7, we have a+b+c=−10+3+7=0 then the value of (−10)3+(3)3+(7)3 is:

(−10)3+(3)3+(7)3=3(−10×3×7)=−630

Hence, (−10)3+(3)3+(7)3=−630