Exercise 29 Page 632

The Product of a Sum and Difference tells us that (a-b)(a+b)=a^2 - b^2.

Exact Solution: 0.8
Approximated Solution: 0.8

Practice makes perfect

To solve the given proportion involving radicals, we will use the Product of a Sum and Difference. (a-b)(a+b)=a^2 - b^2 Let's start by isolating the variable x. We can do this using Cross Products Property.

5/sqrt(8)-2=sqrt(8)+2/x

Cross multiply

5x=(sqrt(8)-2)(sqrt(8)+2)

.LHS /5.=.RHS /5.

x=(sqrt(8)-2)(sqrt(8)+2)/5

(a-b)(a+b)=a^2-b^2

x=(sqrt(8))^2-(2)^2/5

Calculate power

x=(sqrt(8))^2-4/5

( sqrt(a) )^2 = a

x=8-4/5

Subtract term

x=4/5

Write as a decimal

x=0.8

We obtained the exact solution to the equation. We do not need to use a calculator to approximate it to the nearest tenth.

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