Question

please answer these questions.
for 20 points

Answer 1

( ii )

⇒ 8x² + x = 6 - x

⇒ 8x² + x - 6 + x = 0

⇒ 8x² + x + x - 6 = 0

⇒ 8x² + 2x - 6 = 0

Taking out 2 as common,

⇒ 2( 4x² + x - 3 ) = 0

⇒ ( 4x² + x - 3 ) = 0 ÷ 2

⇒ ( 4x² + x - 3 ) = 0

Splitting middle term,

⇒ 4x² + ( 4 - 3 )x - 3 = 0

⇒ 4x² + 4x - 3x - 3 = 0

Taking out 4x as common from first two terms and -3 from last two terms,

⇒ 4x( x + 1 ) -3 ( x + 1 ) = 0

Taking out ( x + 1 ) as common,

⇒ ( x + 1 ) ( 4x - 3 ) = 0

⇒ ( x + 1 ) = 0 ÷ ( 4x - 3 )

⇒ ( x + 1 ) = 0

•°• x = -1

' Or '

⇒ ( x + 1 ) ( 4x - 3 ) = 0

⇒ ( 4x - 3 ) = 0 ÷ ( x + 1 )

⇒ ( 4x - 3 ) = 0

⇒ 4x = 3

•°• x = 3/4

Hence , x is equal to either -1 or 3/4.

( ii )

⇒ 4x² + 13x + ( 15/2 ) = 0

⇒ ( 8x² + 26x + 15 ) / 2 = 0

⇒ ( 8x² + 26x + 15 ) = 0 × 2

⇒ ( 8x² + 26x + 15 ) = 0

Splitting middle term,

⇒ 8x² + ( 20 + 6 )x + 15 = 0

⇒ 8x² + 20x + 6x + 15 = 0

Taking out 4x as common from first two terms and 3 from last two terms,

⇒4x ( 2x + 5 ) + 3 ( 2x + 5 ) = 0

Taking out ( 2x + 5 ) as common,

⇒ ( 2x + 5 ) ( 4x + 3 ) = 0

⇒ ( 2x + 5 ) = 0 ÷ ( 4x + 3 )

⇒ ( 2x + 5 ) = 0

⇒ 2x = -5

•°• x = ( -5/2 )

' Or '

⇒ ( 2x + 5 ) ( 4x + 3 ) = 0

⇒ ( 4x + 3 ) = 0 ÷ ( 2x + 5 )

⇒ ( 4x + 3 ) = 0

⇒ 4x = -3

•°• x = ( -3/4 )

Hence, x is equal to either ( -5/2 ) or ( -3/4 ).

Answer 2

Answer:

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