Question

Find X : using properties of proportion ​

Answer 1

Answer:

x=5/4

Step-by-step explanation:

$\frac{\sqrt{x+1} +\sqrt{x-1} }{\sqrt{x+1} -\sqrt{x-1}}=\frac{4x-1}{2}$

By using Compenedo and Dividendo rule,

$\frac{\sqrt{x+1} +\sqrt{x-1}+\sqrt{x+1} -\sqrt{x-1}}{\sqrt{x+1} +\sqrt{x-1}-\sqrt{x+1}+\sqrt{x-1}}=\frac{4x-1+2}{4x-1-2}\\\frac{2\sqrt{x+1} }{2\sqrt{x-1}}=\frac{4x+1}{4x-3}\\\frac{\sqrt{x+1} }{\sqrt{x-1}}=\frac{4x+1}{4x-3}\\(4x-3)\sqrt{x+1}=(4x+1)\sqrt{x-1}\\(4x-3)^2(x+1)=(4x+1)^2(x-1)\\(16x^2-24x+9)(x+1)=(16x^2+8x+1)(x-1)\\16x^3+16x^2-24x^2-24x+9x+9=16x^3-16x^2+8x^2-8x+x-1\\16x^3-8x^2-15x+1=16x^3-8x^2-7x-1\\-15x+9=-7x-1\\8x=10\\x=5/4$

Hence, x=5/4 is the only solution.