Question

Find x from the following equation using properties of proportion: x2 - x +1 14(x - 1) x2 + x +1 13(x + 1) -​

Answer 1

Step-by-step explanation:

Solution:

\text{Given: } \frac{x^2-x+1}{x^2+x+1} = \frac{14(x-1)}{13(x+1)}\\\\\\

By componendo and dividendo

If \quad \frac ab = \frac cd \quad then\quad \frac {(a+b)}{(a-b)} =\frac {(c+d)}{(c-d)} Now, given equation becomes

\\ \Rightarrow \frac{(x^2-x+1)+(x^2+x+1)}{(x^2-x+1)-(x^2+x+1)} = \frac{14(x-1)+13(x+1)}{14(x-1)-13(x+1)}\\\\\\\ \Rightarrow \frac{x^2-x+1+x^2+x+1}{x^2-x+1-x^2-x-1} =\frac{14x-14+13x+13}{14x-14-13x-13}\\\\\\ \Rightarrow \frac{2x^2+2}{-2x}=\frac{27x-1}{x-27}\\\\\\ \Rightarrow \frac{x^2+1}{-x}=\frac{27x-1}{x-27}\\\\\\ \Rightarrow x^3-27x^2+x-27=-27x^2+x\\\\ \Rightarrow x^3-27=0\\\\ \Rightarrow x^3=27\\\\ \therefore x = 3

Answer 2

Answer:

The value of x is

x = 3

Solution:

Use componendo dividendo

a/b = c/d

Then,

(a+b)/(a-b) = (c+d)/(c-d)

Refer to the solution in the picture below