Question

a3-b3=9 , a-b = 3 find 1/a+1/b​

Answer 1

Step-by-step explanation:

$a^3 - b^3 = 9$

$(a - b)(a^2 + ab + b^2)=9$

$3(a^2 + ab + b^2) = 9$

$(a^2 + ab + b^2)=3$

$(a^2 - 2ab + b^2 + 3ab)=3$

$[(a - b)^2 + 3ab]=3$

$[9 + 3ab] = 3$

$3ab = -6$

$ab = -2$

$(a + b)=\sqrt{(a-b)^2+4ab}$

$(a + b)=\sqrt{9 + 4(-2)}$

$(a + b)=\sqrt{9 - 8}$

$(a + b)=\sqrt{1} = ±1$

$Now ,$

$\frac{1}{a} + \frac{1}{b}$

$\frac{(a + b)}{ab}$

$when , a+b=1$

$then ,$

$\frac{1}{-2}=-\frac{1}{2}$

$if , a+b=-1$

$\frac{-1}{-2}=\frac{1}{2}$