
Concept explainers
To Solve:
√x−3=√x+4−1

Answer to Problem 26PPS
x = 12
Explanation of Solution
Given Information:
Given equation:
√x−3=√x+4−1
Concept Used :
Solve Radical equations:
- Isolate the radical on one side of the equation.
- Raise each side of the equation to a power equal to the index of the radical to eliminate the radical .
- Solve the resulting polynomial equation.Check your results.
- When solving radical equations, the result may be a number that does not satisfy the original equation . Such a number is called an extraneous solution.
Calculation:
- Given √x−3=√x+4−1
√x−3=√x+4−1⇒√x−3−√x+4=−1.........................................[Subtract √x+4 from each side]⇒(√x−3−√x+4)2=(−1)2................................[Squaring each side]⇒x−3+x+4−2√x−3⋅√x+4=1.................[Simplify]⇒2x+1−2√x2+x−12=1⇒−2√x2+x−12=1−1−2x...........................[Subtract (1+2x) from each side]⇒−2√x2+x−12=−2x⇒(−2√x2+x−12)2=(−2x)2.......................[Squaring each side]⇒4(x2+x−12)=4x2⇒4x2+4x−48=4x2⇒4x−48=0....................................[Subtract 4x2from each side]⇒4x=48............................................[Add 48 each side]⇒4x4=484.................................................[Divide each side by 4]⇒x=12
Check :
So, the solution is x = 12
Chapter 6 Solutions
Glencoe Algebra 2 Student Edition C2014
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