Question

me ajuda nessa questão de matématica pfvvvvvv

Answer 1

Resposta:

a)

$a = x^{3}+\frac{1}{x^{3} } \\b = x^{3}-\frac{1}{x^{3} }\\ab = (x^{3}+\frac{1}{x^{3} }).(x^{3}-\frac{1}{x^{3} })\\ab = (x^{3})^2 - (\frac{1}{x^{3}})^2\\ab = x^{6} - \frac{1}{x^{6} } \\ab = \frac{x^{12} - 1}{x^{6} }$

b)

$a = 2x - 1\\b = x + 3\\c = 2x + 1\\ac - b^2 = (2x - 1).(2x+1) - (x+3)^2\\ac - b^2 = (2x)^2 - 1^2 - (x^2 - 2.x.3 + 3^2)\\ac - b^2 = 4x^2 - 1 - (x^2 - 6x + 9)\\ac - b^2 = 4x^2 -1 -x^2 + 6x - 9\\ac - b^2 = 3x^2 + 6x -10$

c)

$x = m + 6\\y = m - 6\\\\x^2 - y^2 + xy = (m+6)^2 - (m-6)^2 + (m+6).(m-6)\\x^2 - y^2 + xy = m^2+2.m.6+6^2 - (m^2 - 2.m.6 + 6^2) + m^2-6^2\\x^2 - y^2 + xy =m^2+12m+36-m^2+12m-36+m^2-36\\x^2 - y^2 + xy =m^2+24m-36$