Question

x^2-(X+2) (X+3)÷7x+1=2÷3​

Answer 1

Answer:

Given that x = 2 + 2^(2/3) + 2^(1/3)

so x - 2 = 2^(2/3) + 2^(1/3)

=(x-2)^3 = [2^(2/3)+2^(1/3)]^3

use (a-b)^3= a^3 - b^3 - 3ab(a-b)

and (a+b)^3= a^3 + b^3 + 3ab(a+b) formulae.

or x^3 - 8 - 6x(x-2) = 2^2 + 2^1 + 3*[2^{(2/3)+(1/3)}[2^(2/3)+2^(1/3)

or x^3 - 8 - 6x^2 + 12x = 4 + 2 + 6(x-2)

or x^3 - 8 -6x^2 + 12x = 6 + 6x - 12

or x^3 - 6x^2 +6x = 2

$\: \: \: \: \: \: \: \: \: \: \: hence \: verified$

Answer 2

$\huge \sf \underbrace {Solution}$

$\sf \rightarrow : \: \frac{x^2-(X+2) (X+3)}{7x+1} = \frac{2}{3}$

$\sf \rightarrow\frac{ {x}^{2} - ( {x}^{2} + 3 x + 2x + 6) }{7x + 1} = \frac{2}{3}$

$\sf \rightarrow : \frac{ {x}^{2} - {x}^{2} - 5x - 6 }{7x + 1} = \frac{2}{3}$

$\sf \rightarrow : \: \frac{ - 5x - 6}{7x + 1} = \frac{2}{3}$

CROSS MULTIPLICATION :

$\sf \bold\rightarrow : \: 5x + 6 \times 3 = 7x + 1 = 2$

$\sf \bold\rightarrow : - 15x + 18 = 14x + 2$

$\sf \bold\rightarrow : - 18 - 2= 14x + 15x$

$\sf \bold\rightarrow : - 29x = 20$

$\huge \sf \bold \rightarrow \pink {x = \frac{20}{29}}$