Question 59

If $$(5\sqrt5 x^3 - 81 \sqrt3 y^3) \div (\sqrt5 x - 3\sqrt3 y) = (Ax^2 + By^2 +Cxy)$$,then the value of $$(6A + B - \sqrt{15} C)$$ is:

Solution

$$(5\sqrt5 x^3 - 81 \sqrt3 y^3) \div (\sqrt5 x - 3\sqrt3 y)$$

Using the formula ,

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

$$(5\sqrt5 x^3 - 81 \sqrt3 y^3) \div (\sqrt5 x - 3\sqrt3 y) $$

= $$5x^2 + 3\sqrt15xy + 9\sqrt{3}y^2$$

A = 5 , B = 27 , C=3$$\sqrt15$$

Putting these values in ,

$$(6A + B - \sqrt{15} C)$$ = 30 + 27 - 45 =12

So , the answer would be Option d)12.

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