What is the answer to sqrt(3x+4)+sqrt(x-4)=2sqrt(x) ?

The answer to sqrt(3x+4)+sqrt(x-4)=2sqrt(x) is x=-4/3 ,x=4

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sqrt(3x+4)+sqrt(x-4)=2sqrt(x)

3 x + 4 + x - 4 = 2 x

x = - \frac{4}{3}, x = 4

Decimal Notation

x = - 1.33333 \dots, x = 4

Solution steps

3 x + 4 + x - 4 = 2 x

Square both sides:

4 x + 2 3 x + 4 x - 4 = 4 x

4 x + 2 3 x + 4 x - 4 = 4 x

Move

4 x

to the left side

2 3 x + 4 x - 4 = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 x + 4 = 0 or x - 4 = 0

Solve

3 x + 4 = 0 : x = - \frac{4}{3}

Solve

x - 4 = 0 : x = 4

x = - \frac{4}{3}, x = 4

Verify Solutions:

x = - \frac{4}{3}

True

, x = 4

True

The solutions are

x = - \frac{4}{3}, x = 4

(7 b^{0.15}) 8 = 2

x = 4 - 3 x

x, \frac{x}{y} + \frac{y}{x} = 6

\frac{196}{7} \cdot \frac{900}{x} = 4

x + 1 + x - 2 = - 1

What is the answer to sqrt(3x+4)+sqrt(x-4)=2sqrt(x) ?
The answer to sqrt(3x+4)+sqrt(x-4)=2sqrt(x) is x=-4/3 ,x=4
Solve for x: sqrt(3x+4)+sqrt(x-4)=2sqrt(x)
The solution is x=-4/3 ,x=4