Evaluate 12abx2 - 9a2 - 8b2x - 6ab - 0- where a- 0 and b- 0-

12ab x ^ 2 ( 9 a ^ 2 8 b ^ 2 ) x 6ab=0 a≠ 0,b≠ 0 Therefore, the roots are: x=( 9 a ^ 2 8 b ^ 2 ) ±√(( 9 a ^ 2 8 b ^ 2 ) #160; ^ 2 +24ab( 12ab ...

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Standard X

Mathematics

Solving a Quadratic Equation by Completion of Squares Method

Evaluate 12...

Question

Evaluate $12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$ , where $a \neq 0$ and $b \neq 0$ .

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Solution

$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0 a \neq 0, b \neq 0$
Therefore, the roots are:
$x = \frac{(9 a^{2} - 8 b^{2}) \pm \sqrt{{(9 a^{2} - 8 b^{2})}^{2} + 24 a b (12 a b)}}{2 \times 12 a b} = \frac{(9 a^{2} - 8 b^{2}) \pm \sqrt{81 a^{4} + 64 b^{4} - 144 a^{2} b^{2} + 288 a^{2} b^{2}}}{24 a b}$
$= \frac{(9 a^{2} - 8 b^{2}) \pm \sqrt{{(9 a^{2} + 8 b^{2})}^{2}}}{24 a b}$
$= \frac{(9 a^{2} - 8 b^{2}) \pm (9 a^{2} + 8 b^{2})}{24 a b}$
$∴ x = \frac{9 a^{2} \times 2}{24 a b} = \frac{3 a}{4 b} o r, x = \frac{- 8 b^{2} \times 2}{24 a b} = \frac{- 2 b}{3 a}$

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12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0

, where a

\neq

0 and b

\neq

12 a b x^{2} - ({9 a}^{2} - {8 b}^{2}) x - 6 a b = 0

Q. Solve for

x

12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0

Solve each of the following quadratic equations:
$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0, w h e r e a \neq 0 a n d b \neq 0$

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Evaluate 12abx2−(9a2−8b2)x−6ab=0, where a≠0 and b≠0.

12abx2−(9a2−8b2)x−6ab=0a≠0,b≠0Therefore, the roots are:x=(9a2−8b2)±√(9a2−8b2)2+24ab(12ab)2×12ab=(9a2−8b2)±√81a4+64b4−144a2b2+288a2b224ab=(9a2−8b2)±√(9a2+8b2)224ab=(9a2−8b2)±(9a2+8b2)24ab∴x=9a2×224ab=3a4bor,x=−8b2×224ab=−2b3a

Evaluate $12 a b x^{2} - (9 a^{2} - 8 b^{2}) x - 6 a b = 0$ , where $a \neq 0$ and $b \neq 0$ .