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If (5√5x3 - 3√3y3) ÷ (√5x - √3y) = (Ax2 + By2 + Cxy), then what is the value of (3A - B - $$\sqrt {15} $$ C)?
Answer & Solution
Correct Answer:
Option
C
$$\eqalign{
& \left( {5\sqrt 5 {x^3} - 3\sqrt 3 {y^3}} \right) \div \left( {\sqrt 5 x - \sqrt 3 y} \right) = A{x^2} + B{y^2} + Cxy \cr
& 3A - B - \sqrt {15} C = ? \cr
& \frac{{{{\left( {\sqrt 5 x} \right)}^3} - {{\left( {\sqrt 3 x} \right)}^3}}}{{\sqrt 5 x - \sqrt 3 y}} = A{x^2} + B{y^2} + Cxy \cr
& 5{x^2} + 3{y^2} + \sqrt {15} xy \cr
& A = 5,\,B = 3,\,C = \sqrt {15} \cr
& 3A - B - \sqrt {15} C \cr
& = 3 \times 5 - 3 - \sqrt {15} \times \sqrt {15} \cr
& = - 3 \cr} $$
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