What is the answer to u^{1/2}+u^{-1/2}=6 ?

The answer to u^{1/2}+u^{-1/2}=6 is u=17+12*2^{1/2},u=17-12*2^{1/2}

Solve for u: u^{1/2}+u^{-1/2}=6

The solution is u=17+12*2^{1/2},u=17-12*2^{1/2}

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u^{\frac{1}{2}} + u^{- \frac{1}{2}} = 6

u = 17 + 12 \cdot 2^{\frac{1}{2}}, u = 17 - 12 \cdot 2^{\frac{1}{2}}

Decimal Notation

u = 33.97056 \dots, u = 0.02943 \dots

Solution steps

u^{\frac{1}{2}} + u^{- \frac{1}{2}} = 6

Expand

u^{\frac{1}{2}} + u^{- \frac{1}{2}} : u^{\frac{1}{2}} + \frac{1}{u ^{\frac{1}{2}}}

u^{\frac{1}{2}} + \frac{1}{u ^{\frac{1}{2}}} = 6

Factor

u^{\frac{1}{2}} + \frac{1}{u ^{\frac{1}{2}}} : \frac{1 + u}{u ^{\frac{1}{2}}}

\frac{1 + u}{u ^{\frac{1}{2}}} = 6

Square both sides:

\frac{1}{u} + 2 + u = 36

\frac{1}{u} + 2 + u = 36

Solve

\frac{1}{u} + 2 + u = 36 : u = 17 + 12 \cdot 2^{\frac{1}{2}}, u = 17 - 12 \cdot 2^{\frac{1}{2}}

u = 17 + 12 \cdot 2^{\frac{1}{2}}, u = 17 - 12 \cdot 2^{\frac{1}{2}}

Verify Solutions:

u = 17 + 12 \cdot 2^{\frac{1}{2}}

True

, u = 17 - 12 \cdot 2^{\frac{1}{2}}

True

The solutions are

u = 17 + 12 \cdot 2^{\frac{1}{2}}, u = 17 - 12 \cdot 2^{\frac{1}{2}}

10 = 14 r + 2

- 1 = 5 x - 1 + 7

2 x + 5 = 2 2 x + 1

3 x^{\frac{1}{2}} = 15

x + 3 + 5 = 12

What is the answer to u^{1/2}+u^{-1/2}=6 ?
The answer to u^{1/2}+u^{-1/2}=6 is u=17+12*2^{1/2},u=17-12*2^{1/2}
Solve for u: u^{1/2}+u^{-1/2}=6
The solution is u=17+12*2^{1/2},u=17-12*2^{1/2}