Question

4x^2-2(a^2+b^2)+a^2b^2=0 find the value of k for quadratic formula, and answers is a^2/2,b^2/2????

Answer 1

Answer:

a²/2, b²/2

Step-by-step explanation:

Given Quadratic Equation is 4x² - 2(a² + b²)x + a²b² = 0

On comparing with ax² + bx + c = 0,

a = 4, b = -2(a² + b²), c = a²b².

∴ D = b² - 4ac

     = [-2(a² + b²)²] - 4(4)(a²b²)

     = [4(a² + b²) - 16(a²b²)]

     = 4[(a² + b²)² - 4a²b²]

     = 4(a² - b²)²

The solutions are:

x = -b ± √D/2a

  = [2(a² + b²) ± √4(a² - b²)²]/8

  = [2(a² + b²) ± 2(a² - b²)]/8

  = [(a² + b²) ± (a² - b²)]/4

  = 2a²/4, 2b²/4

  = a²/2, b²/2

Hope it helps!