If x2 equals 25 y2 equals 16 and z2 equals 9 what is the greatest possible value of Parenthesis xplusy-z parenthesis to the second power?

Answer 1

x2 = 25 therefore x = +/- 5. y2 = 16therefore y = +/- 4. z2 = 9 therefore z = +/- 3. Maximise (x + y - z)2. The expression is at its maximum when (x + y - z) has the greatest possible magnitude - positive or negative. This will happen when z has the opposite sign to x and y. Either (+5) + (+4) - (-3) = 12 or (-5) + (-4) - (+3) = -12. Either way, the square of (x + y - z) is 144.