Question

On solving the quadratic equation,
9x² - 6b²x- ( a⁴ - b⁴) = 0
the value of x is

Answer 1

Answer:

Step-by-step explanation:

Given : 9x² - 6b²x - (a⁴ - b⁴)  = 0

9x² - 6b²x - ((a²)² - (b²)²)  = 0

9x² - 6b²x - (a² - b²) (a² + b²) = 0

9x²  + 3 (a² - b²)x - 3 (a² + b²)x - (a² - b²) (a² + b²) = 0

[3(a² - b²) ×  3 (a² + b²) = 9(a⁴ - b⁴ )  &  3 (a² - b²) - 3 (a² + b²) = - 6b²]

3x [3x(a² - b²)]   - (a² + b²) [3x + (a² - b²) ] = 0

[3x + (a² - b²) ]  [3x - (a² + b²) ] = 0

[3x + (a² - b²) ]  = 0  or     [3x - (a² + b²) ] = 0

3x = - (a² - b²)  or  3x =  (a² + b²)

x = [ - (a² - b²)/3]   or  x = [(a² + b²)/3]

x = (b² - a²)/3  or  x = [(a² + b²)/3]

Hence, the roots of the quadratic equation 9x² - 6b²x - (a⁴ - b⁴)  = 0  are (b² - a²)/3 &  [(a² + b²)/3] .