Question

Resolver √x-1 + √x-7 = 2√x-3
Ecuacion Irracional, para ahora porfa!

El -1,-7 y -3 estan unidos a la raiz

Answer 1

$\sqrt{x-1} + \sqrt{x-7} =2 \sqrt{x-3}$
$( \sqrt{x-1} + \sqrt{x-7})^2=( 2\sqrt{x-3} )^2$
$( \sqrt{x-1} + \sqrt{x-7})^2=4 x-12$
$( \sqrt{x-1} )^2+2 \sqrt{(x-1)(x-7)} +( \sqrt{x-7} )^2=4x-12$
$x-1+2 \sqrt{ x^{2} -7x-x+7} +x-7 = 4x-12$
$2x-8+2 \sqrt{ x^{2} -8x+7} =4x-12$
$2x-8-4x+12+2 \sqrt{ x^{2} -8x+7} =0$
$2 \sqrt{ x^{2} -8x+7} =2x-4$
$(2 \sqrt{ x^{2} -8x+7})^2=(2x-4)^2$
$4x^2-32x+28 =4 x^{2} -16x+16$
$-16x+12 =0$
$x= \frac{12}{16} = \frac{3}4} =0.75$

Comprobación:
$\sqrt{0.75-1} + \sqrt{0.75-7} = 2 \sqrt{0.75-3}$
$\sqrt{-0.25} + \sqrt{-6.25} = 2 \sqrt{-2.25}$
Aplicando la regla de los radicales : $\sqrt{-a} = \sqrt{-1} * \sqrt{a}$
Sabiendo que :$\sqrt{-1} = i$
3 i = 3 i