Question

Find the root of the following 12abx-(9a2-8b)x-6ab=0 Solution

Answer 1

Sol:

12abx2 - (9a2 – 8b2)x – 6ab = 0.

Roots of the quadratic equatios ax2 + bx + c = 0 are

=[-b ± (b2 - 4ac)] / 2a

From the given equation, a = 12ab, b = - (9a2 – 8b2), c = - 6ab


Roots = (9a2 – 8b2) ± √[(9a2 – 8b2)2 + 4(12ab)(6ab)] / 2(12ab)
= (9a2 – 8b2) ± √(81a4 + 64 b4 - 144 a2b2) + (288a2b2)] / 24ab
= (9a2 – 8b2) ± √[(81a4 + 64 b4 + 144 a2b2)] / 24ab
= (9a2 – 8b2) ± √[(9a2 + 8b2)2] / 24ab
= (9a2 – 8b2) ± (9a2 + 8b2) / 24ab

= (9a2 – 8b2) + (9a2 + 8b2) / 24ab, (9a2 – 8b2) - (9a2 + 8b2) / 24ab

= 18a2/ 24ab, – 16b2 / 24ab
= 3a/4b, - 2b/3a

Hence, the roots of the quadratic equation are 3a/4b, - 2b/3a

Answer 2

Step-by-step explanation:

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