Question

√3x+1 - √2x-1 = 1 co posso resolver essa equação

Answer 1

$\sqrt{3x+1} - \sqrt{ 2x-1 } = 1 \\\\ \sqrt{3x+1} =1 + \sqrt{ 2x-1 } \\\\ 3x+1=1+2 \sqrt{2x-1}+2x-1 \\\\ 3x=2 \sqrt{2x-1}+2x-1 \\\\ -2 \sqrt{2x-1} =2x-1-3x \\\\ -2 \sqrt{2x-1} =-x-1 \\\\ 4(2x-1)= x^{2} +2x+1 \\\\ 8x-4= x^{2} +2x+1 \\\\ 8x-4= x^{2} -2x-1=0 \\\\ 6x-5- x^{2} =0 \\\\ - x^{2} +6x-5=0 \\\\ x^{2} +6x+5=0$

$x= \frac{-(-6) \frac{+}{-} \sqrt{(-6)^{2}-4*1*5 } }{2*1} \\\\ x= \frac{6 \frac{+}{-} \sqrt{36-20} }{2} \\\\ x= \frac{6\frac{+}{-} \sqrt{16} }{2} \\\\ x= \frac{6 \frac{+}{-}4 }{2} \\\\ x= \frac{6+4 }{2} \\\\ x= \frac{6-4}{2} \\\\ x_{1} = 1 \\\\ x_{2} = 5$