What statement best describes triangle MON?

Mathematics

1 answer:

frosja888 [35]3 years ago

5 0

Isosceles and a right triangle

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Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.

Paul [167]

Find the powers $a=\sqrt{2}+\sqrt{3}$

$a^{2}=5+2 \sqrt{6}$

$a^{3}=11 \sqrt{2}+9 \sqrt{3}$

The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.

Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$

so fits with the other answers.

3 0

3 years ago

una fracion reducicion a su minima expresion en igual a 1/8 . si la suma de sus terminos es 72. hallar la diferencia entre ellos

Mandarinka [93]

La diferencia entre el denominador y el númerador de la fracción es:

64 - 8 = 56.

<h3>¿Como encontrar la fracción?</h3>

Tendremos una fracción de la forma:

$\frac{a}{b}$