Question

a2 -b2x2_4(b4-3a4)x-12a2b2=0
​

Answer 1

Answer:

X=4b²/a² ,  -3a²/b²

Explanation:

a²b²x² - (4b⁴ - 3a⁴)x - 12a²b² = 0

Here A=a²b²

B= -(4b⁴ - 3a⁴)

C= -  12a²b²

D=discriminant =B²-4AC=

=[( -(4b⁴ - 3a⁴)² - 4 x [a²b²] x -  12a²b²]

=[16b⁸ + 9a⁸ -24a⁴b⁴]+ 48 a⁴ b⁴

=16b⁸ + 9a⁸+24 a⁴ b⁴

=(4b⁴)² +2x 4b x 3a ² + (3a²)²

=(4b⁴+3a⁴)²     [∵ (a+b)²=a²+b²+2ab]

Now, let us use quadratic formula  

X = {-B ± √(B²-4AC)}/2A

= -( -(4b⁴ - 3a⁴)  ±√ (4b⁴+3a⁴)² /2a²b²

={(4b⁴ - 3a⁴)  ± (4b⁴+3a⁴)} /2a²b²

now taking positive sign,

=[(4b⁴ - 3a⁴) + 4b⁴ +3a⁴]/2a²b²

=8b⁴/2a²b²

x=4b²/a²

taking negative value :

=[(4b⁴ - 3a⁴) - 4b⁴ -3a⁴]/2a²b²

=-6a⁴/2a²b²

= -3a²/b²

∴X=4b²/a² ,  -3a²/b²