A line and a square-root curve form a system of equations: their intersection satisfies both equations. A square root is never negative, so first check what that requires of the line. Then graph both original equations in Desmos and click their intersection. Squaring instead can produce a false solution because it erases the sign difference between positive and negative numbers.
Hints
- Hint 1
A square root gives a nonnegative number. At an intersection, the line must have that same value. What does that tell you about ?
- Hint 2
An intersection is a point on both graphs. Graph the two original equations and click where they meet. In a point written , the first number is .
Step-by-step
Graph the original equations
Step 1Use the square root's sign
The principal square root is never negative. At the intersection, it equals , so:
Add to both sides:
Squaring can erase this sign restriction and create a false solution.
- Step 2
Read the intersection's x-coordinate
Type both original equations, and , on separate Desmos lines. Click where they meet; Desmos shows . A coordinate pair lists first, so the requested -value is . It also satisfies . Choice C.