please answer this question......
Answers
Answer:
18 a - b√432 -16b + a√432
------------------- and --------------------
24b 24a
Step-by-step explanation:
12abx² - (9a² - 8b²)x - 6ab = 0
Here, A = 12ab, B = -(9a² - 8b²), C = 6ab
D = B² - 4AC
= -[-(9a² - 8b²)]² - 4 × 12ab × 6ab
= (9a²)² + (8b²)² - 2 × 9a² × 8b² - 4 × 12ab × 6ab [Using (a-b)²]
= 81a power4 + 64b power4 - 144a²b² - 288a²b²
∴D = 81a power4 + 64b power 4 - 432a²b²
x = -B± √D
------------
2A
= -[-(9a² - 8b²)] ± √81a power4 + 64b power 4 - 432a²b²
---------------------------------------------------------------------------------
2A
= 9a² - 8b² ± 9a² + 8b² - ab√432
-------------------------------------------------
2 × 12ab
When D is +ve:
x = 9a² - 8b² + (9a² + 8b² - ab√432)
-----------------------------------------------
24ab
= 18a² - ab√432 a(18a - b√432)
----------------------- = -----------------------
24ab 24ab
= 18a - b√432
------------------- → 1
24b
When D is -ve:
x = 9a² - 8b² - (9a² + 8b² - ab√432)
-----------------------------------------------
24ab
= -16b² + ab√432 b(-16b + a√432)
----------------------- = ------------------------
24ab 24ab
= -16b + a√432
--------------------- →2
24a
Hence, the roots are:
18 a - b√432 -16b + a√432
------------------- and --------------------
24b 24a
Oof... took so long to type xD
Have a good day <3