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

Expert Solution & Answer

Answer to Problem 27WE

The solution of equation are {1,−3}

Explanation of Solution

Given that: : (x−3x+1)2=2.x−3x+1+3

Apply law of Exponents (ab)n=anbn

Rewrite the given equation

(x−3)2(x+1)2=2.x−3x+1+3

Multiply by (x+1)2 , LCM of (x+1)2 and (x+1)

(x+1)2((x−3)2(x+1)2)=(x+1)22.x−3x+1+3(x+1)2

Apply distributive property

(x−3) 2 =2(x+1)(x−3)+3 (x+1) 2 x2−6x+9=2(x2−3x+x−3)+3(x2+2x+1)x2−6x+9=2x2−6x+2x−6+3x2+6x+3x2−6x+9=5x2+2x−3−4x2−8x+12=0−4(x2+2x−3)=0

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

x2+2x−3=0x2+(3−1)x−3=0x2+3x−x−3=0x(x+3)−1(x+3)=0(x−1)(x+3)=0x=1,−3

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

-1 is not in the domain of x cannot be solution.

Check:

For x=1(1−31+1)2=2.1−31+1+3(−1)2=2.(−1)+31=−2+31=1LHS=RHSFor x=−3(−3−3−3+1)2=2.−3−3−3+1+332=2(3)+39=9LHS=RHS

Hence, Solution of equation is {1,−3}

Chapter 5.9, Problem 26WE

Chapter 5.9, Problem 28WE

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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