To solve and check , the given equation has no solution of uu−2+30u+2=9

Expert Solution & Answer

Answer to Problem 19WE

The answer is {1,3}

Explanation of Solution

Given that: : uu−2+30u+2=9

Multiply by (u−2)(u+2) , LCM of (u−2) and (u+2)

(u−2)(u+2)(uu−2+30u+2)=9(u−2)(u+2)

Apply distributive property

(u−2)(u+2)(uu−2+30u+2)=9(u−2)(u+2)u(u+2)+30(u−2)=9(u−2)(u+2)u2+2u+30u−60=9(u2−4)u2+2u+30u−60=9u2−368u2−32u+24=08(u2−4u+3)=0

Apply the factor method

u2−4u+3=0u2−(3+1)u+3=0u2−3u−u+3=0u(u−3)−1(u−3)=0(u−3)(u−1)=0

Apply zero product property to find the solution of equation

(u−3)=0u=3and similarly(u−1)=0u=1

When u equal to 2 and -2, a denominator in the original equation has a value of 0. Therefore,

2 and -2 are not in the domain of u and cannot be solution.

Check:

For u=333−2+303+2=93+6=99=9LHS=RHS

For u=111−2+301+2=9−1+10=99=9LHS=RHS

Hence, the solution of equation is {1,3}

Chapter 5.9, Problem 18WE

Chapter 5.9, Problem 20WE

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

Ch. 5.1 - Prob. 11OE Ch. 5.1 - Prob. 12OE Ch. 5.1 - Prob. 1WE Ch. 5.1 - Prob. 2WE Ch. 5.1 - Prob. 3WE Ch. 5.1 - Prob. 4WE Ch. 5.1 - Prob. 5WE Ch. 5.1 - Prob. 6WE Ch. 5.1 - Prob. 7WE Ch. 5.1 - Prob. 8WE Ch. 5.1 - Prob. 9WE Ch. 5.1 - Prob. 10WE Ch. 5.1 - Prob. 11WE Ch. 5.1 - Prob. 12WE Ch. 5.1 - Prob. 13WE Ch. 5.1 - Prob. 14WE Ch. 5.1 - Prob. 15WE Ch. 5.1 - Prob. 16WE Ch. 5.1 - Prob. 17WE Ch. 5.1 - Prob. 18WE Ch. 5.1 - Prob. 19WE Ch. 5.1 - Prob. 20WE Ch. 5.1 - Prob. 21WE Ch. 5.1 - Prob. 22WE Ch. 5.1 - Prob. 23WE Ch. 5.1 - Prob. 24WE Ch. 5.1 - Prob. 25WE Ch. 5.1 - Prob. 26WE Ch. 5.1 - Prob. 27WE Ch. 5.1 - Prob. 28WE Ch. 5.1 - Prob. 29WE Ch. 5.1 - Prob. 30WE Ch. 5.1 - Prob. 31WE Ch. 5.1 - Prob. 32WE Ch. 5.1 - Prob. 33WE Ch. 5.1 - Prob. 34WE Ch. 5.1 - Prob. 35WE Ch. 5.1 - Prob. 36WE Ch. 5.1 - Prob. 1MRE Ch. 5.1 - Prob. 2MRE Ch. 5.1 - Prob. 3MRE Ch. 5.1 - Prob. 4MRE Ch. 5.1 - Prob. 5MRE Ch. 5.1 - Prob. 6MRE Ch. 5.1 - Prob. 7MRE Ch. 5.1 - Prob. 8MRE Ch. 5.1 - Prob. 9MRE Ch. 5.1 - Prob. 10MRE Ch. 5.1 - 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