Question

Answer the question with a perfect explanation.

Answer 1

Answer:

I hope it is helpful........

Answer 2

$\huge\star{\red{\underline{\mathfrak{Answer}}}}$

Step 1:- Cross multiplication

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

Step 2:- Multiply the equations

$(6 {x}^{6} - 2 {x}^{5} - 10{x}^{4} + 26 {x}^{3}\\\\ - 9 {x}^{2} + 3 {x}^{2} + 15 {x}^{3} - 39 {x}^{2} \\\\+ 3 {x}^{4} - {x}^{3} - 5 {x}^{2} + 13x \\\\+ 3 {x}^{3} - {x}^{2} - 5x + 13) \\\\= (6 {x}^{6} - 2 {x}^{5} + 10 {x}^{4} \\\\ - 26 {x}^{3} - 9 {x}^{4} + 3 {x}^{4} \\\\- 15 {x}^{3} + 39 {x}^{2} - 3 {x}^{4}\\\\ + {x}^{3} - 5 {x}^{2} + 13x - 3 {x}^{3} \\\\ + {x}^{2} - 5x + 13)$

Step 3:- Cut the terms of the equation on both sides of it which has same sign,coefficient and the variable with same power.

So, the equation now shortens.

$( - 10 {x}^{4} + 26 {x}^{3} + 15 {x}^{3} - 39 {x}^{2}\\\\ + 3 {x}^{4} - {x}^{3} + 3 {x}^{3} - {x}^{2})\\\\ = (10 {x}^{4} - 26 {x}^{3} - 15 {x}^{3} + 39 {x}^{2} \\\\- 3 {x}^{4} + {x}^{3} - 3 {x}^{3} + {x}^{2} )$

Step 4:- Shift the terms on the right side to left. This helps in calculating the answer easily.

$( - 10 {x}^{4} + 3 {x}^{4} - 10 {x}^{4} + 3{x}^{4} ) \\\\+ (26 {x}^{3} + 15 {x}^{3} - {x}^{3} \\\\ + 3 {x}^{3} + 26 {x}^{3} + 15 {x}^{3} \\\\- {x}^{3} + 3 {x}^{3} ) + ( - 39 {x}^{2} - \\\\{x}^{2} - 39 {x}^{2} - {x}^{2} ) = 0$

I have also arranged the terms according to their power.

This way you can calculate easily.

Step 5:-Calculate the coefficients of the variable with same power.

$- 14 {x}^{4} + 86 {x}^{3} - 80 {x}^{2} = 0$

Step 6:-If you find any common factor of all the three terms, then remove it for easy calculation.

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

Step 7:-Now, move the common term on right side.

The term will be divide 0, so the answer will be 0.

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

Step 8:-Now take out the value of x.

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

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

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

Therefore,

(7x-8)=0

x=(8/7)

and

(x-5)=0

x=5

So, The values of x are:-

$\huge\boxed{x=(8/7),(5)}$