Question

If (16√2x³ + 81√3y³) ÷ (2√2x + 3√3y) = Ax² + By² + Cxy, then find the value of 2A - 3B - 2√6C.
1. 7
2. 137
3. 25
4. 79

Answer 1

Correct Answer - Option 1 : 7

Given:

⇒ (16√2x3 + 81√3y3) ÷ (2√2x + 3√3y) = Ax2 + By2 + Cxy

Formula:

⇒ a³ + b³ = (a + b)(a² + b² - ab)

Calculation:

⇒ (16√2x3 + 81√3y3) ÷ (2√2x + 3√3y) = Ax2 + By2 + Cxy

⇒ Ax2 + By2 + Cxy = [(2√2x + 3√3y)(8x² + 27y² - 2√2x × 3√3y)]/(2√2x + 3√3y)

⇒ Ax2 + By2 + Cxy = (8x2 + 27y2 - 2√2x × 3√3y)

⇒ Ax2 + By2 + Cxy = (8x2 + 27y2 - 6√6y)

A = 8, B = 27 and C = -6√6

Then,

⇒ ? = 2A - 3B - 2√6C

⇒ ? = 2 × 8 - 3 × 27 - 2√6 × (-6√6)

⇒ ? = 16 - 81 + 72

⇒ ? = 7

∴ 2A - 3B - 2√6C = 7