MathCheck Equation Problem Demo

Solve `sqrt(x) + sqrt(x+1) = sqrt(2x+1)`. equation x = 0 ends f_nodes 5 sqrt(x) + sqrt(x+1) = sqrt(2x+1)

==> /* compute square of both sides */ x + 2 sqrt(x) sqrt(x+1) + x+1 = 2x+1 /* move `x` and `x+1` to the right */ <=> 2 sqrt(x) sqrt(x+1) = 0 /* divide by 2, compute square */ ==> x(x+1) = 0 /* a product is 0 iff any factor is 0 and … */ <=> x = 0 \/ x + 1 = 0 /* move 1 to the right */ <=> x = 0 \/ x = -1 /* check the tentative roots */ original <=> x = 0
or

An alternative solution equation x = 0 ends f_nodes 5 sqrt(x) + sqrt(x+1) = sqrt(2x+1)

<=> x >= 0 /\ x + 2 sqrt(x) sqrt(x+1) + x+1 = 2x+1 /**/ <=> x >= 0 /\ sqrt(x) sqrt(x+1) = 0 /**/ <=> x >= 0 /\ (x=0 \/ x=-1) /**/ /* <=> x=0 \/ x= -1 */
or