Question

a^2b^2x^2-(4b^4-3a^4)x-12a^2b^2 formula method​

Answer 1

Answer:

Step-by-step explanation:

a²b²x² - (4b⁴ - 3a⁴)x - 12a²b² = 0

⇒a²b²x² - 4b⁴x + 3a⁴x - 12a²b² = 0

⇒b²x(a²x - 4b²) + 3a²(a²x - 4b²) = 0

⇒(b²x + 3a²)(a²x - 4b²) = 0

⇒x = 4b²/a², -3a²/b²

Now, using quadratic formula ,

x = {(4b⁴ - 3b⁴) ± √{(4b⁴ -3a⁴)²+48(a²b²)²}}/2a²b²

= {(4b⁴ - 3a⁴) ± √{(4b⁴ + 3a⁴)²}}/2a²b² [ use formula, (x-y)²+4xy=(x+y)²]

= {4b⁴ - 3a⁴ ± (4b⁴ + 3a⁴)}/2a²b²

= 4b²/a², -3a²/b²