What is the answer to 10+24k=13sqrt(1+k^2) ?

The answer to 10+24k=13sqrt(1+k^2) is k=(-240+169sqrt(3))/(407)

Solve for k: 10+24k=13sqrt(1+k^2)

The solution is k=(-240+169sqrt(3))/(407)

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10 + 24 k = 13 1 + k^{2}

k = \frac{- 240 + 169 3}{407}

Decimal Notation

k = 0.12952 \dots

Solution steps

10 + 24 k = 13 1 + k^{2}

Square both sides:

100 + 480 k + 576 k^{2} = 169 + 169 k^{2}

100 + 480 k + 576 k^{2} = 169 + 169 k^{2}

Solve

100 + 480 k + 576 k^{2} = 169 + 169 k^{2} : k = \frac{- 240 + 169 3}{407}, k = - \frac{240 + 169 3}{407}

k = \frac{- 240 + 169 3}{407}, k = - \frac{240 + 169 3}{407}

Verify Solutions:

k = \frac{- 240 + 169 3}{407}

True

, k = - \frac{240 + 169 3}{407}

False

The solution is

k = \frac{- 240 + 169 3}{407}

x^{\frac{3}{2}} = 32

3 x + 6 = x + 5

What is the answer to 10+24k=13sqrt(1+k^2) ?
The answer to 10+24k=13sqrt(1+k^2) is k=(-240+169sqrt(3))/(407)
Solve for k: 10+24k=13sqrt(1+k^2)
The solution is k=(-240+169sqrt(3))/(407)