Question

Si (a^3-b^3)/(a-b)= -ab, calcule Q=(a-b)^3/(a^3-b^3 )

Answer 1

$q = \frac{(a - b) {}^{3} }{a {}^{3} - b {}^{3} }$

$q = \frac{(a - b) {}^{3} }{(a - b)(a {}^{2} + ab + b {}^{2}) }$

$q = \frac{(a - b) {}^{2} }{a {}^{2} + ab + b {}^{2} }$

ahora desarrollamos la condición

si :

$\frac{a {}^{3} - b {}^{3} }{a - b} = - ab$

$\frac{(a - b)(a {}^{2} + ab + b {}^{2}) }{a - b} = - ab$

simplificando

$a {}^{2} + 2ab + b {}^{2} = 0$

$(a + b {}) {}^{2} = 0$

por lo tanto :.

$a = - b$

$q = \frac{4b {}^{2} }{b {}^{2} - b {}^{2} + b {}^{2} }$

simplificando

RESPUESTA:

Q =4