Question

Find the value of k if 1cube+2+3+___+K cube =6084​

Answer 1

Answer:

k=13

explanation :

1^3 +2^3.............+k^3 =6084

apply the formula

[k (k+1)/2]^2 =6084

take square root on both sides

which gives

k(k+1)/2=78

k^2 + k = 78*2

k^2 +k =156

k^2 + k -156 =0

do factorization

which gives

(k +12)(k -13)=0

k=-12 (or) k=13

'k'is an natural number, there for

k=13