Question

2x^-1+x^-1/2 = 6 Find x.​

Answer 1

Answer:

x = 5/2

Step-by-step explanation:

2x + x 1 1/2=6

3x-3/2 = 6

3x = 6 + 3/2

3x = 15/2

x = 5/2

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Answer 2

Step-by-step explanation:

${2x}^{ - 1} + {x}^{ - \frac{1}{2} } = 6$

$\frac{2}{x} + \frac{1}{ \sqrt{x} } = 6$

consider that

$\frac{1}{x} = {p}^{2} and \: \frac{1}{ \sqrt{x} } = p$

then above equation becomes

$2 {p}^{2} + p - 6 = 0$

use formula

$p = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a}$

now

$p = \frac{ - 1± \sqrt{1 - 4 \times 2 \times - 6} }{2 \times 2}$

$p = \frac{ - 1± \sqrt{49} }{4}$

$p = \frac{ - 1±7}{4}$

for positive sign

$p = \frac{6}{4} = \frac{3}{2}$

for negative sign

p= -8/4 = -2

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