# Algebra help

#### cw86

How do you solve equations with radicals in them like this

2√x-3=5

Any help would be great.

#### Prove It

MHF Helper
How do you solve equations with radicals in them like this

2√x-3=5

Any help would be great.
Is this

$$\displaystyle 2\sqrt{x - 3} = 5$$

or

$$\displaystyle 2\sqrt{x} - 3 = 5$$?

cw86

#### cw86

Is this

$$\displaystyle 2\sqrt{x - 3} = 5$$

or

$$\displaystyle 2\sqrt{x} - 3 = 5$$?
I'm sorry its the first one square root

#### Prove It

MHF Helper
$$\displaystyle 2\sqrt{x - 3} = 5$$

$$\displaystyle \sqrt{x - 3} = \frac{5}{2}$$

$$\displaystyle x - 3 = \left(\frac{5}{2}\right)^2$$

$$\displaystyle x - \frac{12}{4} = \frac{25}{4}$$

$$\displaystyle x = \frac{37}{4}$$.

cw86

#### skeeter

MHF Helper
How would you solve for radius a with only knowing radius b and the length of x?

at this website Tangent circles, Common external tangent line, Geometric Mean. Elearning.

draw a segment parallel to CD from point B to AC ... let the intersection point with AC be point E.

right triangle ABE ... vertical leg = a-b , horizontal leg = x , hypotenuse = a+b

now use Pythagoras to get the desired result.

... btw, next time start a new problem w/ a new thread.

cw86

#### cw86

draw a segment parallel to CD from point B to AC ... let the intersection point with AC be point E.

right triangle ABE ... vertical leg = a-b , horizontal leg = x , hypotenuse = a+b

now use Pythagoras to get the desired result.

... btw, next time start a new problem w/ a new thread.

That wont work cause I don't know how long a is.

#### sa-ri-ga-ma

That wont work cause I don't know how long a is.
No need to know a. According to Pythagoras

$$\displaystyle (a+b)^2 = x^2 + (a - b)^2$$

Simplify the above equation to get the result.

cw86

#### cw86

No need to know a. According to Pythagoras

$$\displaystyle (a+b)^2 = x^2 + (a - b)^2$$

Simplify the above equation to get the result.
Lets say Radius b is 2 and line x is 5 what would the radius of a be?,I'm not understanding how you can solve it with the Pythagorean Theorem.

Last edited:

#### sa-ri-ga-ma

Lets say Radius b is 2 and line x is 5 what would the radius of a be?,I'm not understanding how you can solve it with the Pythagorean Theorem.
In the problem no numerical values are included. You have to prove

$$\displaystyle x = 2\sqrt(ab)$$

cw86