Question 41521
{{{sqrt(x+4)-2sqrt(x-1)=-1)}}}
{{{sqrt(x+4) = -1 + 2sqrt(x-1)}}}
{{{(sqrt(x+4))^2 = (-1 + 2sqrt(x-1))^2}}}
{{{x + 4 = 1 - 4sqrt(x-1) + 4(x-1)}}}
{{{x + 4 = 1 - 4sqrt(x-1) + 4x - 4}}}
{{{x + 4 = -4sqrt(x-1) + 4x - 3}}}
{{{-3x + 7 = -4sqrt(x-1)}}}
{{{(3/4)x - (7/4) = sqrt(x-1)}}}
{{{((3/4)x - (7/4))^2 = (sqrt(x-1))^2}}}
{{{(9/16)x^2 - (42/16)x + (49/16) = x - 1}}}
{{{9x^2 - 42x + 49 = 16x - 16}}}
{{{9x^2 - 58x + 65 = 0}}}
*[invoke quadratic "x", 9, -58, 65]
{{{x = 5}}} and {{{x = 13/9}}}
Check:
{{{sqrt(x+4)-2sqrt(x-1)=-1)}}}
{{{sqrt(5+4)-2sqrt(5-1)=-1)}}}
{{{sqrt(9)-2sqrt(4)=-1)}}}
{{{3-2(2)=-1)}}}
{{{3-4=-1)}}} Five Works
Check:
{{{sqrt(x+4)-2sqrt(x-1)=-1)}}}
{{{sqrt((13/9)+4)-2sqrt((13/9)-1)=-1)}}}
{{{sqrt((13/9)+(36/9))-2sqrt((13/9)-(9/9))=-1)}}}
{{{sqrt(49/9)-2sqrt(4/9)=-1)}}}
{{{(7/3)-2(2/3)=-1)}}}
{{{(7/3)-(4/3)=-1)}}}
{{{(3/3)=-1)}}} (13/9) Does Not Work