Problem 49967. When the sum of the cubes is a quartic...

Created by Doddy Kastanya

Solve Later

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The answer should be put in a vector where the first \"num\" entries are the values of a's and the last entry is b. 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<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 182px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 91px; transform-origin: 407px 91px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Consider the following equality:</span></span></div><div style="block-size: 80px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 40px; text-align: left; transform-origin: 384px 40px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" 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" data-image-state="image-loaded"></div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">For a given value of n (i.e., num in the problem statement), determine the values of a's and b that satisfy the equality above. The answer should be put in a vector where the first "num" entries are the values of a's and the last entry is b. There is no unique answer to each of the problems; however, you answer will be checked against the requirement.</span></span></div></div></div>

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