Question

find The Roots of the following equations:
I) x/8+8/=x/2+2/x
2) 2x+1/x+1=x+8/x+4
​

Answer 1

Answer:

$2)sol {}^{n}$

$\frac{2x + 1}{x + 1} = \frac{x + 8}{x + 4}$

$=>(2x + 1)(x + 4)=(x+ 8)(x+1)$

$= > 2x {}^{2} + 8x + x + 4 = x {}^{2} + x + 8x + 8$

$= > x {}^{2} = 4$

$= > x = \sqrt{4}$

$so \: \: x = 2 \: \: or \: - 2$

Answer 2

Answer:

1) The roots of the equation are x = 4 and x = - 4.

2) The roots of the equation are x = 2 and x = - 2.

Step-by-step-explanation:

1)

The given equation is

( x / 8 ) + ( 8 / x ) = ( x / 2 ) + ( 2 / x )

⇒ ( x² + 64 ) / 8x = ( x² + 4 ) / 2x

⇒ x² + 64 = ( x² + 4 ) * 8x / 2x

⇒ x² + 64 = ( x² + 4 ) * 4

⇒ x² + 64 = 4x² + 16

⇒ 64 - 16 = 4x² - x²

⇒ 3x² = 48

⇒ x² = 48 / 3

⇒ x² = 16

⇒ x = ± √16

⇒ x = ± 4

∴ The roots of the equation are x = 4 and x = - 4.

─────────────────────

2)

The given equation is

( 2x + 1 ) / ( x + 1 ) = ( x + 8 ) / ( x + 4 )

⇒ ( 2x + 1 ) ( x + 4 ) = ( x + 8 ) ( x + 1 )

⇒ 2x ( x + 4 ) + 1 ( x + 4 ) = x ( x + 1 ) + 8 ( x + 1 )

⇒ 2x² + 8x + x + 4 = x² + x + 8x + 8

⇒ 2x² + 9x + 4 = x² + 9x + 8

⇒ 2x² + 4 = x² + 8

⇒ 2x² - x² = 8 - 4

⇒ x² = 4

⇒ x = ± √4

⇒ x = ± 2

∴ The roots of the equation are x = 2 and x = - 2.