What is the answer to 10=u^{1.1}+u^{0.8}+u^{0.5} ?

The answer to 10=u^{1.1}+u^{0.8}+u^{0.5} is u=4.17653…

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10=u^{1.1}+u^{0.8}+u^{0.5}

10 = u^{1.1} + u^{0.8} + u^{0.5}

u = 4.17653 \dots

Solution steps

10 = u^{1.1} + u^{0.8} + u^{0.5}

Use the following exponent property

: a^{n} = (a^{\frac{1}{m}})^{(n \cdot m)}

u^{1.1} = (u^{\frac{1}{2}})^{(1.1 \cdot 2)}, u^{0.8} = (u^{\frac{1}{2}})^{(0.8 \cdot 2)}

10 = (u^{\frac{1}{2}})^{\frac{11}{5}} + (u^{\frac{1}{2}})^{\frac{8}{5}} + u^{\frac{1}{2}}

Rewrite the equation with

u^{\frac{1}{2}} = v

10 = v^{\frac{11}{5}} + v^{\frac{8}{5}} + v

Solve

10 = v^{\frac{11}{5}} + v^{\frac{8}{5}} + v : v = 2.04365 \dots

v = 2.04365 \dots

Substitute back

v = u^{\frac{1}{2}},

solve for

u

Solve

u^{\frac{1}{2}} = 2.04365 \dots : u = 4.17653 \dots

u = 4.17653 \dots

Verify Solutions:

u = 4.17653 \dots

True

The solution is

u = 4.17653 \dots

x - 1 = 7 - x

x - 8 x - 16 = 0

x^{2} + x + 2 x^{2} + x - 3 = 3

2 n = 3 n - 1

5 x^{\frac{3}{2}} - 25 = 0

What is the answer to 10=u^{1.1}+u^{0.8}+u^{0.5} ?
The answer to 10=u^{1.1}+u^{0.8}+u^{0.5} is u=4.17653…
Solve for u: 10=u^{1.1}+u^{0.8}+u^{0.5}
The solution is u=4.17653…