What is the answer to 6u^{-1/2}-13u^{-1/4}+6=0 ?

The answer to 6u^{-1/2}-13u^{-1/4}+6=0 is u= 81/16 ,u= 16/81

Solve for u: 6u^{-1/2}-13u^{-1/4}+6=0

The solution is u= 81/16 ,u= 16/81

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6 u^{- \frac{1}{2}} - 13 u^{- \frac{1}{4}} + 6 = 0

u = \frac{81}{16}, u = \frac{16}{81}

Decimal

u = 5.0625, u = 0.19753 \dots

Solution steps

6 u^{- \frac{1}{2}} - 13 u^{- \frac{1}{4}} + 6 = 0

Expand

6 u^{- \frac{1}{2}} - 13 u^{- \frac{1}{4}} + 6 : \frac{6}{u ^{\frac{1}{2}}} - \frac{13}{u ^{\frac{1}{4}}} + 6

\frac{6}{u ^{\frac{1}{2}}} - \frac{13}{u ^{\frac{1}{4}}} + 6 = 0

Use the following exponent property

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

u^{\frac{1}{2}} = (u^{\frac{1}{4}})^{\frac{4}{2}}

\frac{6}{( u ^{\frac{1}{4}} ) ^{2}} - \frac{13}{u ^{\frac{1}{4}}} + 6 = 0

Rewrite the equation with

u^{\frac{1}{4}} = v

\frac{6}{v ^{2}} - \frac{13}{v} + 6 = 0

Solve

\frac{6}{v ^{2}} - \frac{13}{v} + 6 = 0 : v = \frac{3}{2}, v = \frac{2}{3}

v = \frac{3}{2}, v = \frac{2}{3}

Substitute back

v = u^{\frac{1}{4}},

solve for

u

Solve

u^{\frac{1}{4}} = \frac{3}{2} : u = \frac{81}{16}

Solve

u^{\frac{1}{4}} = \frac{2}{3} : u = \frac{16}{81}

u = \frac{81}{16}, u = \frac{16}{81}

Verify Solutions:

u = \frac{81}{16}

True

, u = \frac{16}{81}

True

The solutions are

u = \frac{81}{16}, u = \frac{16}{81}

- 11 3 x + 13 = - 20

2 x + 1 = x - 7

x = 0.6

2 + r = 11

2 6 - x = 0

What is the answer to 6u^{-1/2}-13u^{-1/4}+6=0 ?
The answer to 6u^{-1/2}-13u^{-1/4}+6=0 is u= 81/16 ,u= 16/81
Solve for u: 6u^{-1/2}-13u^{-1/4}+6=0
The solution is u= 81/16 ,u= 16/81