What is the answer to sqrt(k+1)+sqrt(k)=3sqrt(k) ?

The answer to sqrt(k+1)+sqrt(k)=3sqrt(k) is k= 1/3

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sqrt(k+1)+sqrt(k)=3sqrt(k)

k + 1 + k = 3 k

k = \frac{1}{3}

Decimal Notation

k = 0.33333 \dots

Solution steps

k + 1 + k = 3 k

Remove square roots

4 k^{2} + 4 k = 49 k^{2} - 14 k + 1

Solve

4 k^{2} + 4 k = 49 k^{2} - 14 k + 1 : k = \frac{1}{3}, k = \frac{1}{15}

k = \frac{1}{3}, k = \frac{1}{15}

Verify Solutions:

k = \frac{1}{3}

True

, k = \frac{1}{15}

False

The solution is

k = \frac{1}{3}

\frac{x ^{2} + 3}{x} = 2 x

x + 2 x + 1 = 13

x + 3 + x = 3

x^{2} + x + 1 = x + 1

5 + 2 x - 7 = x

What is the answer to sqrt(k+1)+sqrt(k)=3sqrt(k) ?
The answer to sqrt(k+1)+sqrt(k)=3sqrt(k) is k= 1/3
Solve for k: sqrt(k+1)+sqrt(k)=3sqrt(k)
The solution is k= 1/3