Question

Q. 8. Solve the following quadratic equation for x :
9x² - 6b² x – (a⁴ – b⁴) = 0​

Answer 1

Answer:

Step-by-step explanation:

Solution :

9x² - 6b²x - ( a⁴ - b⁴ ) = 0

=> 9x² - 6b²x - ( a²+b² )( a² - b² ) = 0

=> 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

=> x = ( a² + b² )/3 or x = ( b² - a² )/3

Answer 2

Answer:

9x²-6b²x-(a⁴-b⁴)=0

9x² - 6b²x - (a²+b²)(a²-b²) = 0

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

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

[3x+(a²-b²)][3x-(a²+b²)]=0

∴x = (a²+b²)/3  and  (b²-a²)/3