What is the answer to sqrt(z+3)-sqrt(3z)-1=0 ?

The answer to sqrt(z+3)-sqrt(3z)-1=0 is z=(5-sqrt(21))/2

Solve for z: sqrt(z+3)-sqrt(3z)-1=0

The solution is z=(5-sqrt(21))/2

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z + 3 - 3 z - 1 = 0

z = \frac{5 - 21}{2}

Decimal Notation

z = 0.20871 \dots

Solution steps

z + 3 - 3 z - 1 = 0

Remove square roots

4 z^{2} - 8 z + 4 = 12 z

Solve

4 z^{2} - 8 z + 4 = 12 z : z = \frac{5 + 21}{2}, z = \frac{5 - 21}{2}

z = \frac{5 + 21}{2}, z = \frac{5 - 21}{2}

Verify Solutions:

z = \frac{5 + 21}{2}

False

, z = \frac{5 - 21}{2}

True

The solution is

z = \frac{5 - 21}{2}

4 - x = x + 2

x - 1 + 2 - x = 1

21 + 4 x = x

x - 1 = 5 - x

What is the answer to sqrt(z+3)-sqrt(3z)-1=0 ?
The answer to sqrt(z+3)-sqrt(3z)-1=0 is z=(5-sqrt(21))/2
Solve for z: sqrt(z+3)-sqrt(3z)-1=0
The solution is z=(5-sqrt(21))/2