Find 3 consecutive odd numbers where the product of the smaller two numbers is 46 less than the square of the largest number.
Accepted Solution
A:
Answer: The numbers are: " 5, 7, and 9 " . ___________________________________________________
Explanation: ___________________________________________________ Let the "3 consecutive odd numbers" be represented by: ___________________________________________________ "x" ; ___________________________________________________ "x + 2 " ; ___________________________________________________ "x + 4 " ; ___________________________________________________ → Solve for "x" ; and then solve for "(x + 2)" and "(x + 4)" . ___________________________________________________
The product of the smaller two numbers, is "46 less than" (the square of) the largest number: ___________________________________________________ → " x* (x + 2) = (x + 4)² − 46 " ; ___________________________________________________ Note the "distributive property" of multiplication: ___________________________________________________ a(b + c) = ab + ac ;
a(b − c) = ab − ac . ___________________________________________________
Start with simplifying the "left-hand side" of the equation: ___________________________________________________
" x(x + 2)" = (x * x) + (x * 2 ) = (x² + 2x) ; ___________________________________________________ Then simplify the "right-hand side" of the equation: ___________________________________________________