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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

9. Proofs Using Coordinate Geometry

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Exercise 38 Page 418

Consider the positive and negative solutions when isolating a variable raised to the power of two.

8 and - 8

Practice makes perfect

We will solve the given equation by taking the square roots. Remember to consider the positive and negative solutions.

r^2-3 = 61

LHS+3=RHS+3

r^2 = 64

sqrt(LHS)=sqrt(RHS)

sqrt(r^2)=sqrt(64)

sqrt(a^2)=± a

r=±sqrt(64)

Calculate root

r=± 8

We found that r=± 8. Thus, there are two solutions for the equation, which are r= 8 and r= - 8.

Checking Our Answer

Checking our answer

We can check our answers by substituting them for r in the given equation. Let's start with r=- 8.

r^2-3=61

r= - 8

( - 8)^2-3? =61

▼

Simplify

NegBaseToPosPow

(- a)^2 = a^2

8^2-3? =61

Calculate power

64-3? =61

Subtract term

61=61 ✓

Since 61=61, we know that r=- 8 is a solution of the equation. Let's check if r=8 is also a solution.

r^2-3=61

r= 8

8^2-3? =61

▼

Simplify

Calculate power

64-3? =61

Subtract term

61=61 ✓

Again, since 61=61, we know that r=8 is a solution of the equation.

Subchapter links

Lesson Check p.416

Standardized Test Prep p.418

Mixed Review p.418