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Cube-Root of a Negative Perfect Cube

If x =√13+2√3...

Question

If $x = \sqrt{13} + 2 \sqrt{3}$ , find the value of $x - \frac{1}{x}$

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Solution

$g i v e n x equals square root of 13 plus 2 square root of 3 t h e n 1 over x equals fraction numerator 1 over denominator square root of 13 plus 2 square root of 3 end fraction space space space space equals fraction numerator 1 over denominator square root of 13 plus 2 square root of 3 end fraction cross times fraction numerator square root of 13 minus 2 square root of 3 over denominator square root of 13 minus 2 square root of 3 end fraction space space space space equals fraction numerator square root of 13 minus 2 square root of 3 over denominator 13 minus 12 end fraction space space space equals square root of 13 minus 2 square root of 3 t h e n x minus 1 over x equals square root of 13 plus 2 square root of 3 minus open parentheses square root of 13 minus 2 square root of 3 close parentheses space space space space space space space space space space equals 4 square root of 3$

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x = \sqrt{13} + 2 \sqrt{3}

, find the value of

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If 2x+3y=13 and xy=6 find the value of 8x³+27y³.

Q. If 2x+3y = 13 and xy = 6, find the value of 8x³ + 27y³

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Cube-Root of a Negative Perfect Cube

Standard VIII Mathematics

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