Question

Hello please solve this fastest and accurate answer will be marked the brainliest♎️ ♎️ ♎️ ♎️

Answer 1

Answer:

(a/a² + b²), (-1/a)

Step-by-step explanation:

Given Equation is a(a² + b²)x² + b²x - a = 0

On comparing with ax² + bx + c = 0, we get

a = a(a² + b²), b = b², c = -a.

∴ D = b² - 4ac

      = (b²)² - 4(a³ + ab²)(-a)

      = b⁴ + 4a⁴ + 4a²b²

The solutions are:

⇒ x = -b ± √D/2a

     = [(-b²) ± √b⁴ + 4a⁴ + 4a²b²]/2a(a² + b²)

     = [-b² ± (b² + 2a²)²]/2a(a² + b²)

(i)

-b² + (b² + 2a²)/2a(a² + b²)

= (-b² + b² + 2a²)/2a(a² + b²)

= 2a²/2a(a² + b²)

= (a/a² + b²).

(ii)

-b - (b² + 2a²)/2a(a² + b²)

= (-b² - b² - 2a²)/2a(a² + b²)

= (-2b² - 2a²)/2a(a² + b²)

= -2(a² + b²)/2a(a² + b²)

= (-1/a).

Hope it helps!