Question

Find the real solutions of the equation. 2 + 74x 3 = x Select the correct choice below. O A. {1,7} OB. {-7} Oc. {2} OD. {-1} O E. {1}

Answer 1

$\\\\2 + \sqrt{4x -3}= x \\\\x-2 = \sqrt{4x-3}$

Now squaring both sides we get

$\\\\(x-2)^2 = {4x-3} \\\\x^2 -4x+4= 4x-3 \\\\x^2 -4x-4x+4+3=0 \\\\x^2 -8x+7=0 \\\\x^2-7x-x+7=0 \\\\x(x-7)-1(x-7)=0 \\\\(x-1)(x-7)=0 \\\\x=1,7$

Now 1 satisfy the given equation when we take the negative value of the root and 7 satisfy the given equation when we take the positive value of the root.