If (5sqrt5x³-3√(3)y³)÷(√(2)x - sqrt3y)=(Ax² +By²+Cxy) , then what is the value of 3\ (A - B-sqrt15C)?

If (5sqrt5x³-3√(3)y³)÷(√(2)x - sqrt3y)=(Ax² +By²+Cxy)…

If $(5\sqrt5x^3-3\sqrt 3y^3)÷(\sqrt 2x - \sqrt3y)=(Ax^2 +By^2+Cxy)$ , then what is the value of $3\ (A - B-\sqrt15C)?$

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e -3.

Given:

(5√5x³- 3√3y³) + (√5x - √3y) = (Ax² + By² + Cxy)

Identity used:

(a³ - b³) = (a - b) × (a² + b² + ab)

Calculation:

(5√5x³ - 3√3y³) = (√5x)³ - (√3y)³

(√5x)³- (√3y)³ = (√5x - √3y) x (5x² + 3y² + √15xy)

As, (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 we'll get

⇒ A = 5, B = 3 and C = √15

According to the question, we have to find 3A - B - √15C

⇒ 3A - B - √15C = 3 x 5 - 3 - √15 × √15

⇒ 3A - B - √15C is -3