If $7 a - 5 b = 6$ and $a b = 9$ , find the value of $343 a^{3} - 125 b^{3}$

5126

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636

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5226

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5886

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Solution

The correct option is D $5886$
$7 a - 5 b = 6$
Squaring both sides,
$=> (7 a - 5 b)^{2} = 6^{2}$
$=> 49 a^{2} + 25 b^{2} - 2 (7 a) (5 b) = 36$
$=> 49 a^{2} + 25 b^{2} - 70 (9) = 36$
$=> 49 a^{2} + 25 b^{2} = 36 + 630$
$=> 49 a^{2} + 25 b^{2} = 666$
Now,
$= (7 a)^{3} - (5 b)^{3}$
$= (7 a - 5 b) [(7 a)^{2} + (7 a) (5 b) + (5 b)^{2}]$
$= 6 (49 a^{2} + 35 (9) + 25 b^{2})$
$= 6 (666 + 315)$
$= 5886$

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