If 1x-3-2x-2-8x- then find the value of x- - 3 marks-

1(x 3)+2(x 2)=8x x 2+2(x 3)((x 3)(x 2))+2(x 2)=8x ⇒(3x 8)(x 3)(x 2) =8x [ 1 Mark] On cross multiplying we get, ⇒x(3x 8)=8(x 3)(x 2) ⇒3x^2 8x=8(x^2 5x+6) ⇒8x^2 ...

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Byju's Answer

Standard X

Mathematics

Multiplication of Matrices

If 1x-3+2x-2=...

Question

If $\frac{1}{(x - 3)} + \frac{2}{(x - 2)} = \frac{8}{x}$ , then
find the value of $x$ .
[ 3 marks]

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Solution

$\frac{1}{(x - 3)} + \frac{2}{(x - 2)} = \frac{8}{x}$
$\frac{x - 2 + 2 (x - 3)}{((x - 3) (x - 2))} + \frac{2}{(x - 2)} = \frac{8}{x}$
$\Rightarrow \frac{(3 x - 8)}{(x - 3) (x - 2)} = \frac{8}{x}$ [ 1 Mark]

On cross multiplying we get,
$\Rightarrow x (3 x - 8) = 8 (x - 3) (x - 2)$
$\Rightarrow 3 x^{2} - 8 x = 8 (x^{2} - 5 x + 6)$
$\Rightarrow 8 x^{2} - 40 x + 48 - (3 x^{2} - 8 x) = 0$
$\Rightarrow 5 x^{2} - 32 x + 48 = 0$
$\Rightarrow 5 x^{2} - 20 x - 12 x + 48 = 0$
$\Rightarrow 5 x (x - 4) - 12 (x - 4) = 0$
$\Rightarrow (x - 4) (5 x - 12) = 0$
Now, either $x - 4 = 0 \Rightarrow x = 4$
Or, $5 x - 12 = 0 \Rightarrow x = \frac{12}{5}$ [ 1 mark]

Thus, the roots of the given quadratic equation are $\frac{12}{5}$ and $4$ respectively [ 1 mark]

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If 1(x−3)+2(x−2)=8x, then find the value of x. [ 3 marks]

If $\frac{1}{(x - 3)} + \frac{2}{(x - 2)} = \frac{8}{x}$ , then
find the value of $x$ .
[ 3 marks]