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MATH / If the number (1)/(2)((5)/(root[3](3)+root[3](2))+(1)/(root[3](3)−root[3](2)))can be expressed in the form root[3](a)+root[3](b), where a and b are integers, compute a+b.

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

If the number 12(533+23+133−23)\frac{1}{2} \left(\frac{5}{\sqrt[3]{3} + \sqrt[3]{2}} + \frac1{\sqrt[3]{3} -\sqrt[3]{2}}\right)can be expressed in the form a3+b3,\sqrt[3]{a} + \sqrt[3]{b}, where aa and bb are integers, compute a+b.a+b.
Plain-text mathematical notation (without MathML)
If the number (1)/(2)((5)/(root[3](3)+root[3](2))+(1)/(root[3](3)−root[3](2)))can be expressed in the form root[3](a)+root[3](b), where a and b are integers, compute a+b.
Original LaTeX notation
If the number \[\frac{1}{2} \left(\frac{5}{\sqrt[3]{3} + \sqrt[3]{2}} + \frac1{\sqrt[3]{3} -\sqrt[3]{2}}\right)\]can be expressed in the form $\sqrt[3]{a} + \sqrt[3]{b},$ where $a$ and $b$ are integers, compute $a+b.$

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
3da5390f-3dd5-5389-8a0b-08dd5c769f04
task_key
intermediate~5falgebra--test--3da5390f-3dd5-5389-8a0b-08dd5c769f04
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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