Radical Expressions and Equations

Radical Equations


Solve the equation x+15=9. \sqrt{ x+ 15 } = 9.

Solve the equation

6x+27=x. \sqrt{ 6 x + 27 } = x.

Solve for xx:

x+1415x+85=2 \sqrt{x+141} - \sqrt{ 5x+85} = 2

The solution to the equation 1+1x4x2=x 1 + \sqrt{1 - \sqrt{x^4-x^2}} = x can be written in the form ab \frac{a}{b} where aa and bb are coprime positive integers. Find a+ba+b.

If 180+x29=3,\frac{\sqrt{180+x}}{\sqrt{29}}=3, what is the value of xx?


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