f (5 \\sqrt{5} x^{3}-81 \\sqrt{3} y^{3} ) \\div(\\sqrt{5} x-3 \\sqrt{3} y) = (A x^{2}+B y^{2}+C x y ), then the value of (6 A+B-\\sqrt{15} C) is

SSC CGL 4 06 2019 Shift 1 Paper

Question : 59 of 100

Marks: +1, -0

f\ (5 \√{5} x^{3}-81 \√{3} y^{3}\ ) \÷(\√{5} x-3 \√{3} y)

=\ (A x^{2}+\

B y^{2}+C x y

), then the value of

(6 A+B-\√{15} C)

Solution:

\ {(\√{5} x)^{3}-(3 \√{3})^{3}}/{\√{5} x-3 \√{3} y}=\ (A x^{2}+B y^{2}+C x y\ )

5 x^{2}+27 y^{2}+3 \√{15} x y=A x^{2}+B y^{2}+C x y

A=5

B=27

C=3 \√{15}

6 A+B-\√{15} C

=6 \×5+27 \. \√{15} \×3 \√{15}

=57-45

=12

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