Chapter 9.5, Problem 49PFA

(A)

To determine

Find the solution.

Answer to Problem 49PFA

False

Explanation of Solution

Given Information: $x^2-x-7=-4$

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

Calculation:

  $x^2-x-7=-4$

Put $x=-1$

  ${\left(-1\right)}^2-\left(-1\right)-7=-4$

So,

  $1+1-7=-4$

Now, simplify

  $-5\ne -4$

Put $x=3$

  $3^2-3-7=-4$

So,

  $9-3-7=-4$

Now, simplify

  $-1\ne -4$

(B)

To determine

Find the solution.

Answer to Problem 49PFA

False

Explanation of Solution

Given Information: $x^2-2x+7=-4$

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

Calculation:

  $x^2-2x+7=-4$

Put $x=-1$

  ${\left(-1\right)}^2-2\left(-1\right)+7=-4$

So,

  $1+2+7=-4$

Now, simplify

  $10\ne -4$

Put $x=3$

  $3^2-2\left(3\right)+7=-4$

So,

  $9-6+7=-4$

Now, simplify

  $10\ne -4$

(C)

To determine

Find the solution.

Answer to Problem 49PFA

True

Explanation of Solution

Given Information: $x^2-2x-7=-4$

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

Calculation:

  $x^2-2x-7=-4$

Put $x=-1$

  ${\left(-1\right)}^2-2\left(-1\right)-7=-4$

So,

  $1+2-7=-4$

Now, simplify

  $-4=-4$

Put $x=3$

  ${\left(3\right)}^2-2\left(3\right)-7=-4$

So,

  $9-6-7=-4$

Now, simplify

  $3-7=-4$

Hence,

  $-4=-4$

(D)

To determine

Find the solution.

Answer to Problem 49PFA

False

Explanation of Solution

Given Information: $2x^2-14x-14=-4$

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

Calculation:

  $2x^2-14x-14=-4$

Put $x=-1$

  $2{\left(-1\right)}^2-14\left(-1\right)-14=-4$

So,

  $2+14-14=-4$

Now, simplify

  $2\ne -4$

Put $x=3$

  $2{\left(3\right)}^2-14\left(3\right)-14=-4$

So,

  $18-42-14=-4$

Now, simplify

  $-38\ne -4$