Chapter 9.1, Problem 6PSA

a

To determine

To calculate: The Value of xin the given expression i.e. $x^2+16=25$

Answer to Problem 6PSA

Values of x are $-3$ and $3$ .

Explanation of Solution

Given information:$x^2+16=25$

Formula used: $a^2-b^2=(a+b)(a-b)$

Calculation: $x^2+16=25$

  $\begin{array}{l}\Rightarrow x^2+16-25=0\\ \Rightarrow x^2-9=0\\ $ \Rightarrow x^2-{(3)}^2=0$\Rightarrow (x+3)(x-3)=0\end{array}$

  $\Rightarrow x+3=0$ and $x-3=0$

  $\Rightarrow x=-3$ and $x=3$

b

To determine

To calculate: The Value of xin the given expression i.e. $x^2+6^2=100$

Answer to Problem 6PSA

Values of x are $8$ and $-8$ .

Explanation of Solution

Given information:$x^2+6^2=100$

Formula used: $a^2-b^2=(a+b)(a-b)$

Calculation: $x^2+6^2=100$

  $\begin{array}{l}\Rightarrow x^2+6^2={10}^2\\ \Rightarrow x^2={10}^2-6^2\\ \Rightarrow x^2=(10+6)(10-6)\\ \Rightarrow x^2=(16)(4)\\ \Rightarrow x^2=64\\ \Rightarrow x=\sqrt{64}\\ \Rightarrow x=\pm 8\end{array}$

  $\Rightarrow x=8$ and $x=-8$

c

To determine

To calculate: The Value of xin the given expression i.e. ${12}^2+x^2={13}^2$

Answer to Problem 6PSA

Values of x are $5$ and $-5$ .

Explanation of Solution

Given information:${12}^2+x^2={13}^2$

Formula used: $a^2-b^2=(a+b)(a-b)$

Calculation: ${12}^2+x^2={13}^2$

  $\begin{array}{l}\Rightarrow x^2={13}^2-{12}^2\\ \Rightarrow x^2=(13+12)(13-12)\\ \Rightarrow x^2=(25)(1)\\ \Rightarrow x^2=25\\ \Rightarrow x=\sqrt{25}\\ \Rightarrow x=\pm 5\end{array}$

  $\Rightarrow x=5$ and $x=-5$

d

To determine

To calculate: The Value of xin the given expression i.e. $x^2+{(3\sqrt{3})}^2=36$

Answer to Problem 6PSA

Values of x are $3$ and $-3$ .

Explanation of Solution

Given information:$x^2+{(3\sqrt{3})}^2=36$

Calculation: $x^2+{(3\sqrt{3})}^2=36$

  $\begin{array}{l}\Rightarrow x^2+27=36\\ \Rightarrow x^2=36-27\\ \Rightarrow x^2=9\\ \Rightarrow x=\sqrt{9}\\ \Rightarrow x=\pm 3\end{array}$

  $\Rightarrow x=3$ and $x=-3$

e

To determine

To calculate: The Value of xin the given expression i.e. ${(\sqrt{5})}^2+{(\sqrt{11})}^2=x^2$

Answer to Problem 6PSA

Values of x are $4$ and $-4$ .

Explanation of Solution

Given information:${(\sqrt{5})}^2+{(\sqrt{11})}^2=x^2$

Calculation: ${(\sqrt{5})}^2+{(\sqrt{11})}^2=x^2$

  $\begin{array}{l}\Rightarrow 5+11=x^2\\ \Rightarrow x^2=16\\ \Rightarrow x=\sqrt{16}\\ \Rightarrow x=\pm 4\end{array}$

  $\Rightarrow x=4$ and $x=-4$

f

To determine

To calculate: The Value of xin the given expression i.e. $x^2={(5\sqrt{3})}^2+{(\sqrt{5})}^2$

Answer to Problem 6PSA

Values of x are $4\sqrt{5}$ and $-4\sqrt{5}$ .

Explanation of Solution

Given information:$x^2={(5\sqrt{3})}^2+{(\sqrt{5})}^2$

Calculation: $x^2={(5\sqrt{3})}^2+{(\sqrt{5})}^2$

  $\begin{array}{l}\Rightarrow x^2=75+5\\ \Rightarrow x^2=80\\ \Rightarrow x=\sqrt{80}\\ \Rightarrow x=\pm 4\sqrt{5}\end{array}$

  $\Rightarrow x=4\sqrt{5}$ and $x=-4\sqrt{5}$