If ( 5√5x3 - 3√3y3) ÷ ( √5x - √3y ) = ( Ax2 + By2 + Cxy), then the value of ( 3A + B - √15C) is :
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 3
(5√5x3 - 3√3y3) ÷ (√5x - √3y) = (Ax2 + By2 + Cxy)
(a3 - b3) = (a - b)(a2 + b2 + ab)
(5√5x3 - 3√3y3) = (√5x)3 - (√3y)3
(√5x)3 - (√3y)3 = (√5x - √3y)(5x2 + 3y2 + √15xy)
(5√5x3 - 3√3y3)/(√5x - √3y) = (Ax2 + By2 + Cxy)
[(√5x - √3y)(5x2 + 3y2 + √15xy)]/(√5x - √3y) = Ax2 + By2 + Cxy
5x2 + 3y2 + √15xy = Ax2 + By2 + Cxy
Comparing both sides -
A = 5
B = 3
C = √15
3A - B - √15C = 3 × 5 - 3 - √15 × √15 = 15 - 3 -15 = -3