Question

a , b, c and d are consecutive natural numbers and a3 = b3 + c3 + d3 , what is the least value of a ? (Solve by trial and error method​

Answer 1

Step-by-step explanation:

if thing 9it happens bi9

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Answer 2

Answer:

6

Step-by-step explanation:

a 3 =b 3 +c 3 +d 3

is possible for consecutive natural numbers only if a>b>c>d

Therefore, b=(a−1),c=(a−2),d=(a−3)

⇒a 3 =(a−1) 3 +(a−2) 3 +(a−3) 3

a cannot be 3 as this will make d=0 and it is given in the question that all a,b,c,d are natural numbers

Substituting for a from the answer option, starting with the least number

If a=6, then LHS=a

3 =3 3 =216, andRHS= (a−1) 3 +(a−2) 3 +(a−3) 3 =5 3 +4 3 +3 3=125+64+27=216

We can see LHS=RHS

We can stop here as we want the least value for a.

Hence, 6 is the correct answer.