Question

qrt{x-1} +\sqrt{x+2} = \sqrt{2x-3}" alt="\sqrt{x-1} +\sqrt{x+2} = \sqrt{2x-3}" align="absmiddle" class="latex-formula"> x=?

Answer 1

Answer:

$x = \frac{ - 2 + - \sqrt{ - 176} }{10}$

Step-by-step explanation:

attached

Answer 2

Answer:

• x = 2

Step-by-step explanation:

See the steps:

• $\sqrt{x-1} +\sqrt{x+2} =\sqrt{2x-3}$
• x - 1 + x + 2 + 2$\sqrt{({x-1)(x+2)}$ = 2x - 3
• 2x + 1  + 2$\sqrt{x^2+x -2}$ = 2x - 3
• 2$\sqrt{x^2+x -2}}$ = -4
• $\sqrt{x^2+x-2}$ = -2
• x² + x - 2 = 4
• x² + x - 6 = 0
• x = (-1 ±$\sqrt{1-4(-6)}$)/2
• x = (-1 ± 5)/2
• x = -3, discounted as it leads to negative root
• x = 2