If 8x⁶ - 6√(6)y⁶ = (2x² + Ay²)(4x⁴ + Bx²y² + Cy⁴), then what is the value of (A² - B² + C²)?

If 8x⁶ - 6√(6)y⁶ = (2x² + Ay²)(4x⁴ + Bx²y² + Cy⁴), then…

If 8x⁶ - $6\sqrt{6}y^6$ = (2x² + Ay²)(4x⁴ + Bx²y² + Cy⁴), then what is the value of (A² - B² + C²)?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 18.

a³ - b³ = (a - b)(a² + ab + b²)

8x⁶ - 6√6y⁶ = (2x² + Ay²)(4x⁴ + Bx²y² + Cy⁴)

⇒ (2x² - √6y²)(4x⁴ + 2√6x²y² + 6y⁴) = (2x² + Ay²)(4x⁴ + Bx²y² + Cy⁴)

Now, comparing the equation

A = -√6; B = 2√6; C = 6

A² - B² + C² = (-√6)² - (2√6)² + 6² = 6 - 24 + 36 = 18