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Questions and Answers
Which of the following is a radical equation?
Which of the following is a radical equation?
- x=3
- squr x+3=13 (correct)
- squr x+11=15
- 7squr x=14 (correct)
What is the value of x if (8x-8)^(3/2)=64?
What is the value of x if (8x-8)^(3/2)=64?
3
What is the value of x in squr x+11=15?
What is the value of x in squr x+11=15?
4
What is the value of x in squr 1-3x=x+3?
What is the value of x in squr 1-3x=x+3?
What are the possible values of x in x=2+squ x-2?
What are the possible values of x in x=2+squ x-2?
What is the solution for x in squr -3x-2=x+2?
What is the solution for x in squr -3x-2=x+2?
What is the value of x in squr 2x+4=16?
What is the value of x in squr 2x+4=16?
What is the value of x in squr 4x+41=x+5?
What is the value of x in squr 4x+41=x+5?
What is the solution for x in 3squr x+8=-4?
What is the solution for x in 3squr x+8=-4?
What does (45-3x)^(1/2)=x-g yield for x?
What does (45-3x)^(1/2)=x-g yield for x?
What does SQUR x+10-1=x simplify to?
What does SQUR x+10-1=x simplify to?
What is the value of x in squr x^2+81=x+10?
What is the value of x in squr x^2+81=x+10?
What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base?
What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base?
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Study Notes
Radical Equations Overview
- Radical equations involve roots, typically expressed with variables under a radical sign.
- Example: ( \sqrt{x} + 11 = 15 ).
Examples of Radical Equations
- ( 7\sqrt{x} = 14 ) is a fundamental radical equation.
- ( (8x-8)^{3/2} = 64 ) can be simplified to find ( x = 3 ).
- For ( \sqrt{1-3x} = x + 3 ), the solution is ( x = -1 ).
- The equation ( x = 2 + \sqrt{x-2} ) yields solutions ( x = 2 ) or ( x = 3 ).
- In ( \sqrt{-3x-2} = x + 2 ), the solution is ( x = -6 ).
Advanced Radical Equations
- ( \sqrt{2x + 4} = 16 ) has the solution ( x = 126 ).
- The equation ( \sqrt{4x + 41} = x + 5 ) gives ( x = -8 ).
Identifying Radical Equations
- Determine if the equation contains a radical. Example: ( \sqrt{x} + 3 = 13 ).
Evaluating Complex Equations
- For ( 3\sqrt{x} + 8 = -4 ), solving leads to ( x = -72 ).
- The expression ( (45 - 3x)^{1/2} = x - g ) has a solution of ( x = 3 ).
Simplifying Radical Equations
- The equation ( \sqrt{x + 10} - 1 = x ) can be rearranged to ( x + 10 = x^2 + 2x + 1 ).
- In ( \sqrt{x^2 + 81} = x + 10 ), the rearrangement leads to ( x^2 + 81 = x^2 + 20x + 100 ).
Real-world Application
- A 15-foot ladder placed 3.5 feet from a wall reaches a height of 14.6 feet according to the ladder height equation.
Repetition of Solutions
- ( \sqrt{-3x-2} = x + 2 ) repeats with ( x = -6 ) as its solution, emphasizing the importance of checking for extraneous roots.
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