Example 2: x=10
Example 3: x=-1
Example 4: x=35
Example 5: a-b+c=9
Example 6: x=1, x=1/2
Further explanation:
Example 2:
[tex]\sqrt{4x-4} =6[/tex]
Taking Square on both sides
[tex](\sqrt{4x-4})^2 =(6)^2\\4x-4=36\\4x=36+4\\4x=40\\\frac{4x}{4}=\frac{40}{4}\\x=10[/tex]
Example 3:
[tex]9+\sqrt{4x+8}=11[/tex]
Subtracting 9 from both sides
[tex]9-9+\sqrt{4x+8}=11-9\\\sqrt{4x+8}=2\\[/tex]
Taking Square on both sides
[tex](\sqrt{4x+8})^2=(2)^2\\4x+8=4\\4x=4-8\\4x=-4\\\frac{4x}{4}=-\frac{4}{4}\\x=-1[/tex]
Example 4:
[tex]8+\sqrt{x+1}=2[/tex]
subtracting 8 from both sides
[tex]8-8+\sqrt{x+1}=2-8\\\sqrt{x+1}=-6[/tex]
Taking Square on both sides
[tex](\sqrt{x+1})^2=(-6)^2\\x+1=36\\[/tex]
Subtracting 1 from both sides
[tex]x+1-1=36-1\\x=35[/tex]
Example 5:
[tex]\sqrt{a-b+c}=3[/tex]
Taking Square on both sides
[tex](\sqrt{a-b+c})^2=(3)^2\\a-b+c=9\\[/tex]
Example 6:
[tex]2\sqrt{2x-1}=4x-2[/tex]
Taking square on both sides
[tex](2\sqrt{2x-1})^2=(4x-2)^2\\4(2x-1)=16x^2+4-16x\\8x-4=16x^2-16x+4\\8x=16x^2-16x+4+4\\8x=16x^2-16x+8\\16x^2-16x-8x+8=0\\16x^2-24x+8=0[/tex]
dividng whole equation by 8
[tex]2x^2-3x+1=0\\2x^2-2x-x+1=\\2x(x-1)-1(x-1)=0\\(2x-1)(x-1)=0\\2x-1=0 => x=\frac{1}{2}\\x-1=0 => x=1[/tex]
Keywords: Radical Expressions, Examples
Learn more about radical expressions at:
- brainly.com/question/8145673
- brainly.com/question/10071175
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