Question

using quadratic formula solve the equation a^2b^2x^2-(4b^4-3a^4)x-12a^2b^2=0

solve for x

Answer 1

Answer:

Solutions are x = 4b²/a²  and  x = -3a²/b²

Step-by-step explanation:

Quadratic formula says solutions for

Ax² + Bx + C = 0

are x = ( - B ± √Δ ) / (2A),  where Δ = B² - 4AC is the discriminant.

For the given quadratic in the problem, the discriminant then is

Δ = ( 4b⁴ - 3a⁴ )² - 4 (a²b²) (-12a²b²)

= ( 4b⁴ - 3a⁴ )² + 48a⁴b⁴

= ( 4b⁴ + 3a⁴ )².

So the solutions of the quadratic in question are

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

= 8b⁴ / ( 2a²b² )     OR     -6a⁴ / ( 2a²b² )

= 4b²/a²    OR    -3a²/b².

That this is correct can then be easily checked with a computer algebra system or something online like wolframalpha (see screenshot).  There we see that yes, indeed, the factorization shows that these are precisely the solutions that we were asked for.

Hope that helps.