If a – b = 3 and ab = 10, find : a^3 – b^3. - Vidyadip

Question

If $a – b = 3$ and $ab = 10$, find : $a^3 – b^3.$

✓

Answer

$a − b = 3$
$\Rightarrow (a − b)^3 = (3)^3$
$\Rightarrow a^3 − b^3 − 3ab (a − b) = 27$
$\Rightarrow a^3 − b^3− 3\times 10 (3) = 27$
$\Rightarrow a^3 − b^3− 90 = 27$
$\Rightarrow a^3 − b^3 = 27 + 90$
$\Rightarrow a^3 − b^3 = 117$
Alternative Method :
$(a − b)^3 = a^3− b^3 − 3ab (a − b)$
$\Rightarrow (3)^3= a^3 − b^3− 3\times 10 (3)$
$\Rightarrow 27 = a^3− b^3− 90$
$\Rightarrow 27 + 90 = a^3 − b^3$
$\Rightarrow 117 = a^3 − b^3$
$\Rightarrow a^3 − b^3 = 117$

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