Question

find the roots of the following equations: please tell me​

Answer 1

Question:

Find the roots of the following equations

1) 2 / 3x = ( x - 1 ) / ( 2x - 1 )

2) x / ( 2 + 1 ) = 12 / x

Answer:

1) The roots of the equation are x = 2 and x = 1 / 3.

2) The roots of the equation are x = 6 and x = - 6.

Step-by-step-explanation:

1)

The given equation is

2 / 3x = ( x - 1 ) / ( 2x - 1 )

⇒ 2 ( 2x - 1 ) = 3x ( x - 1 )

⇒ 4x - 2 = 3x² - 3x

⇒ 3x² - 3x - 4x + 2 = 0

⇒ 3x² - 7x + 2 = 0

⇒ 3x² - 6x - x + 2 = 0

⇒ 3x ( x - 2 ) - 1 ( x - 2 ) = 0

⇒ ( x - 2 ) ( 3x - 1 ) = 0

⇒ ( x - 2 ) = 0 OR ( 3x - 1 ) = 0

⇒ x - 2 = 0 OR 3x - 1 = 0

⇒ x = 2 OR 3x = 1

⇒ x = 2 OR x = 1 / 3

∴ The roots of the equation are x = 2 and x = 1 / 3.

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2)

The given equation is

x / ( 2 + 1 ) = 12 / x

⇒ x / 3 = 12 / x

⇒ x * x = 12 * 3

⇒ x² = 36

⇒ x = ± √36

⇒ x = ± 6

∴ The roots of the equation are x = 6 and x = - 6.