What is the answer to 4sqrt(t^2+4)=5t ?

The answer to 4sqrt(t^2+4)=5t is t= 8/3

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4sqrt(t^2+4)=5t

4 t^{2} + 4 = 5 t

t = \frac{8}{3}

Decimal Notation

t = 2.66666 \dots

Solution steps

4 t^{2} + 4 = 5 t

Square both sides:

16 t^{2} + 64 = 25 t^{2}

16 t^{2} + 64 = 25 t^{2}

Solve

16 t^{2} + 64 = 25 t^{2} : t = \frac{8}{3}, t = - \frac{8}{3}

t = \frac{8}{3}, t = - \frac{8}{3}

Verify Solutions:

t = \frac{8}{3}

True

, t = - \frac{8}{3}

False

The solution is

t = \frac{8}{3}

x, 3 - 2 x = x

4 x = 4

4 x = 0

4 x = 2 x - 4

x, 1 + x + 1 = y