Which two signs should be interchanged to make the given equation correct?

$171÷3-16+72\times 412=572$

To determine which two signs should be interchanged to make the given equation correct, we start with the original equation:

$171÷3-16+72\times 412=572$

We are given the correct option to interchange is × and –. Let's swap the multiplication sign ($\times$) and the subtraction sign ($-$) in the equation and verify the result.

Substituting the signs, the new equation becomes:

$171÷3\times 16+72-412=572$

Now, we simplify the left-hand side (LHS) of the equation using the BODMAS rule (Bracket, Of, Division, Multiplication, Addition, Subtraction):

Step 1: Perform the Division
Divide 171 by 3:
$171÷3=57$

Substitute this back into the equation:
$57\times 16+72-412$

Step 2: Perform the Multiplication
Multiply 57 by 16:
$57\times 16=912$

Substitute this value back:
$912+72-412$

Step 3: Perform the Addition
Add 912 and 72:
$912+72=984$

Substitute this value back:
$984-412$

Step 4: Perform the Subtraction
Subtract 412 from 984:
$984-412=572$

Since the LHS equals the RHS (572 = 572), the equation is correct. Therefore, the signs that must be interchanged are indeed × and –.