Question

2x +7/x+2 = 4x+3/2x-7 find x^4+x^2+x+1​

Answer 1

Answer:

Given,

$\frac{2x+7}{x + 2} = \frac{4x + 3}{2x -7}$

$(2x + 7)(2x -7) = (4x + 3)(x + 2)$

$4x^2 - 49 = 4x^2 + 8x + 3x + 6$

$4x^2 - 49 = 4x^2 + 11x + 6$

$4x^2 - 4x^2 = 11x + 6 + 49$

$11x + 55 = 0$

$11x = -55$

$x = -5$

∴   $x^4+x^2+x+1 = (-5)^4 + (-5)^2 + (-5) +1$

                           $= 625 + 25 - 5 + 1$

                           $= 646$

                Hope it helps you^_^