Solve the equations- 2x3 - 3x2 - x - 12x3 -3x2 - x - 1 - 3x3 - x2 - 5x - 133x3 - x2 - 5x - 13-

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Solve the equ...

Question

Solve the equations:
$\frac{2 x^{3} - 3 x^{2} + x + 1}{2 x^{3} - 3 x^{2} - x - 1} = \frac{3 x^{3} - x^{2} + 5 x - 13}{3 x^{3} - x^{2} - 5 x + 13}$ .

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Solution

$\frac{2 x^{3} - 3 x^{2} + x + 1}{2 x^{3} - 3 x^{2} - x - 1} = \frac{3 x^{3} - x^{2} + 5 x - 13}{3 x^{3} - x^{2} - 5 x + 13}$

Using dividendo and componendo

$\frac{2 x^{3} - 3 x^{2} + x + 1 + (2 x^{3} - 3 x^{2} - x - 1)}{2 x^{3} - 3 x^{2} + x + 1 - (2 x^{3} - 3 x^{2} - x - 1)} = \frac{3 x^{3} - x^{2} + 5 x - 13 + (3 x^{3} - x^{2} - 5 x + 13)}{3 x^{3} - x^{2} + 5 x - 13 - (3 x^{3} - x^{2} - 5 x + 13)}$

$\frac{4 x^{3} - 6 x^{2}}{2 x + 2} = \frac{6 x^{3} - 2 x^{2}}{10 x - 26}$

Here we see that $x$ is common both the equations, So $x = 0$ is the solution,

$\frac{2 x - 3}{x + 1} = \frac{3 x - 1}{5 x - 13}$

$10 x^{2} - 15 x - 26 x + 39 = 3 x^{2} - x + 3 x - 1$

$7 x^{2} - 43 x + 40 = 0$

$7 x^{2} - 35 x - 8 x + 40 = 0$

$(7 x - 8) (x - 5) = 0$

$x = 5, \frac{8}{7}, 0$ are the solutions.

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Similar questions

${lim}_{x \to \infty} \frac{3 x^{3} - 4 x^{2} + 6 x - 1}{2 x^{3} + x^{2} - 5 x + 7}$

Q. Find the derivative of

y (x) = \frac{x^{3}}{(x + 1)^{2}}

with respect to

x

Consider the system of equations
$x_{1} + 2 x_{2} + 3 x_{3} = 1$
$x_{2} + 2 x_{3} + 3 x_{1} = 2$
$x_{3} + 2 x_{1} + 3 x_{2} = 3$
then

A. $x_{1} = \frac{2}{3}$

B. $x_{1} + x_{2} = \frac{4}{3}$

C. $x_{3} = - \frac{1}{3}$

D. $x_{1} - x_{2} = \frac{1}{3}$

Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

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Solve the equations:2x3−3x2+x+12x3−3x2−x−1=3x3−x2+5x−133x3−x2−5x+13.

Solve the equations:
$\frac{2 x^{3} - 3 x^{2} + x + 1}{2 x^{3} - 3 x^{2} - x - 1} = \frac{3 x^{3} - x^{2} + 5 x - 13}{3 x^{3} - x^{2} - 5 x + 13}$ .