Chapter 3.5, Problem 47STP

To determine

To find greatest possible value of ${(x-y)}^2$ .If $x^2=25$ and $y^2=9$ .

Answer to Problem 47STP

  ${(x-y)}^2=4$

Explanation of Solution

Given information:

Expression

  $x^2=25$

  $y^2=9$

Greatest possible value of ${(x-y)}^2$

Calculation:

Expression

  $x^2=25$

  $y^2=9$

On solving each expression

  $x=\sqrt{25}$

  $y=\sqrt{9}$

On solving each expression

  $x=\pm 5$

  $y=\pm 3$

Greatest values

  $x=5$

  $y=3$

Then greatest possible value

  ${(x-y)}^2={(5-3)}^2$

On solving

  $={(2)}^2$

On solving

  ${(x-y)}^2=4$