Chapter 9.5, Problem 1CYU

To determine

Find the value of c.

Answer to Problem 1CYU

  $c=81$

Explanation of Solution

Given Information: $x^2-18x+c$

Formula Used: $a^2-2ab+b^2={(a-b)}^2$

Calculation:

  $x^2-18x+c$

So, simplify and make the factor of -18

  $x^2-\left(2\times x\times 9\right)+c$  (1)

As, $a^2-2ab+b^2={(a-b)}^2$

Compare equation (1) with $a^2-2ab+b^2={(a-b)}^2$

  $a=x$ and $b=9$

Put value of a and b in $a^2-2ab+b^2={(a-b)}^2$

  $x^2-\left(2\times x\times 9\right)+9^2={(x-9)}^2$  (2)

Now, compare equation (1) and (2)

  $c=9^2$

Hence,

  $c=81$