Question

1/15x^2+5/3=2/3x solve this equation


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Answer 1

Answer:

Step-by-step explanation:

1 / (15 x^2) + (5 / 3)= (2 / 3x )

⇒ ( 1 × 1 )+ ( 5x ^2 × 5 ) / 15x^2 = ( 2 / 3x )

⇒ 1 + 25x ^2 / 15x^2 = ( 2 / 3x )

⇒ By using cross multiplication, we get

⇒ 3x ( 1 + 25x ^2 ) = 15x^2 ( 2 )

⇒ ( 3x × 1 ) + ( 3x × 25x ^2 ) = 30x^2

⇒ 3x + 75x ^3 = 30x^2

⇒ 75x ^3 + 3x = 30x^2

⇒ 75x^3 - 30x^2 + 3x = 0

⇒ 3 ( 25x ^3 - 10x ^2 + x ) = 0 (∵ taken by 3 common)

⇒ 25x ^3 -10x ^2 + x = 0 ( ∵25 × 1 =25, -5 × -5 = 25, -5 -5 = -10 )

⇒ 25x ^3 -5x ^2 - 5x ^2 + x = 0

⇒ 5x ^2 ( 5x - 1 ) - x ( 5x - 1 ) = 0

⇒ ( 5x ^2 - x ) ( 5x - 1 ) = 0

⇒5x ^2 - x = 0 or 5x - 1 = 0

⇒ 5x ^2 = x or 5x = 1

⇒ x = 5x ^2 or x = 1 / 5

⇒ x = 5 (1/5) ^2 or x = 1/5

⇒ x = 5 × ( 1 / 25 ) or x = 1 / 5

⇒ x = 5 / 25 or x = 1 / 5

⇒ x = 1 / 5 or x = 1 / 5

∴ x = 1 / 5 is the answer.