Find the Ramanujan number for the following: $8^{3} + ? = 36^{3} + ?$ .

64^{3}

and

60^{3}

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44^{3}

and

60^{3}

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64^{3}

and

50^{3}

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24^{3}

and

50^{3}

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Solution

The correct option is A $64^{3}$ and $60^{3}$
Ramanujan number expressible as the sum of two cubes in two different ways.
So,
$8^{3} + 64^{3} = 36^{3} + 60^{3}$
$512 + 262144 = 46656 + 216000$
$262656 = 262656$

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Find the Ramanujan number for the following: 83+?=363+?.

The correct option is A 643 and 603Ramanujan number expressible as the sum of two cubes in two different ways.So, 83+643=363+603512+262144=46656+216000262656=262656

Find the Ramanujan number for the following: $8^{3} + ? = 36^{3} + ?$ .

The correct option is A $64^{3}$ and $60^{3}$
Ramanujan number expressible as the sum of two cubes in two different ways.
So,
$8^{3} + 64^{3} = 36^{3} + 60^{3}$
$512 + 262144 = 46656 + 216000$
$262656 = 262656$