To solve and check , the given equation has no solution of (t+3t−1)2=2+t+3t−1

Expert Solution & Answer

Answer to Problem 28WE

The solution of equation are {−1,5}

Explanation of Solution

Given that: : (t+3t−1)2=2+t+3t−1

Apply law of Exponents (ab)n=anbn

Rewrite the given equation

(t+3)2(t−1)2=2+t+3t−1

Multiply by (t−1)2 , LCM of (t−1)2 and (t−1)

(t−1)2((t+3)2(t−1)2)=2.(t−1)2+t+3t−1(t−1)2

Apply distributive property

(t+3) 2 =2 (t−1) 2 +(t+3)(t−1)t2+6t+9=2(t2−2t+1)+(t2−t+3t−3)t2+6t+9=2t2−4t+2+t2+2t−3t2+6t+9=3t2−2t−1−2t2+8t+10=0t2−4t−5=0

Apply the factor method and Apply zero product property to find the solution of equation

t2−4t−5=0t2−(5−1)t−5=0t2−5t+t−5=0t(t−5)+1(t−5)=0(t+1)(t−5)=0x=−1,5

When t equal to 1, a denominator in the original equation has a value of 0. Therefore,

1 is not in the domain of t cannot be solution.

Check:

For t=−1(−1+3−1−1)2=2+−1+3−1−1(2−2)2=2+2−2(−1)2=2+(−1)1=2−11=1LHS=RHSFor t=5(5+35−1)2=2+5+35−122=2+24=4LHS=RHS

Hence, Solution of equation is {−1,5}

Chapter 5.9, Problem 27WE

Chapter 5.9, Problem 29WE

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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