3^3 + 4^3 +5^3 = nbsp;(1^3 +2^3+ 3^3 + 4^3 +5^3) nbsp;(1^3 +2^3) 1^3 +2^3+ 3^3 + 4^3 +5^3 = 15^2nbsp; [ ∵ 1^3+2^3+...n^3 = (1+2+...n)^3] Similarly, n ...

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Byju's Answer

Standard VIII

Mathematics

Differences of Squares of Triangular Numbers and Converse

33 + 43 +53 =

Question

$3^{3} + 4^{3} + 5^{3}$ =

216

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212

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214

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Solution

The correct option is A 216
$3^{3} + 4^{3} + 5^{3}$ = ( $1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3}$ ) - ( $1^{3} + 2^{3}$ )

$1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3}$ = $15^{2}$ $[∵ 1^{3} + 2^{3} + . . . n^{3} = (1 + 2 + . . . n)^{3}]$

Similarly, $1^{3} + 2^{3} = 3^{2}$

$∴ 3^{3} + 4^{3} + 5^{3} = 15^{2} - 3^{2}$
$= 225 - 9$
$= 216$

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Similar questions

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33 + 43 +53 =

The correct option is A 21633 + 43 +53 = (13 +23+ 33 + 43 +53) - (13 +23) 13 +23+ 33 + 43 +53 = 152[ ∵13+23+...n3=(1+2+...n)3] Similarly, 13 +23=32 ∴33 + 43 +53=152−32 =225−9 =216

$3^{3} + 4^{3} + 5^{3}$ =