Question

solve 12abx²-9a²x+8b²x-6ab

Answer 1

$12abx ^{2} - 9a^{2} x + 8b^{2}x - 6ab \\ = 3ax(4bx - 3a) + 2b(4bx - 3a) \\ = (3ax + 2b)(4bx - 3a)$

Answer 2

GIVEN:-

$\rm \underline{ \underline{12abx {}^{2} - (9a {}^{2} - 8b {}^{2} )x - 6ab = 0}}$

TO FIND OUT:-

$x = {?}$

SOLUTION:-

$\rm \: comparing \: the \: given \: equation \: with \: Ax {}^{2} + Bx + C = 0 \: \: we \: get$

$\rm \: A=12ab , \rm \: B=-(9a²-8b²),C=-6ab</u></strong><strong><u>$

$\rm \: using \: quadratic \: formula \: we \: get</u></strong><strong><u>\</u></strong><strong><u>\</u></strong><strong><u>$

$\large \rm \: x = \frac{ - B∓ \sqrt{B²-4AC} }{2A} </u></strong><strong><u>$

$\rm \: x = -[ - (9a²-8b²)]∓ \frac{ \sqrt{[ - (9a²-8b²) - 4(12ab)( - 6ab)}</u></strong><strong><u> }{2(12ab)}$

$\large \rm \: x= \frac{9a²-8b²∓ \sqrt{81a² + 64b²-144a²b²+288a²b²} </u></strong><strong><u>}{24ab}$

$\large \rm \: x = \frac{9a²-8b²∓ \sqrt{81a⁴ + 64b⁴ + 144a²b²} </u></strong><strong><u>}{24ab}$

$\large \rm \: x = \frac{9a²-8b²∓ \sqrt{(9a²+8b²)²} }{24ab}$

$\large \rm \:x= \frac{9a²-8b²∓(9a²+8b²)}{24b}$

$\large\rm \: x = \frac{9a²-8b² + 9a² + 8b²}{24ab} or \: x= \frac{9a²-8b²-9a²-8b²}{24ab}$

$\large \rm \: x = \frac{18a²}{24b²} , \frac{ - 16b²}{24ab}$

$\rm \boxed{ \therefore \: x = \frac{3a}{4b} , \frac{ - 2b}{3a} }$