Question

please solve all Question
factorise ( given in the picture​​

Answer 1

QuestioN :

Factorise the following :

i ) 6√3x² - 47x + 5√3.

ii ) 7x² + 2√14x + 2.

iii ) √2x² + 3x + √2.

iv ) x² + 3√3x + 6.

v ) 4√3x² + 5x - 2√3.

SolutioN :

i ) 6√3x² - 47x + 5√3.

→ 6√3x² - 47x + 5√3.

→ 6√3x² - 45x - 2x + 5√3.

→ 3√3x( 2x - 5√3 ) - 1 ( 2x - 5√3 )

→ ( 3√3 - 1 )( 2x - 5√3 )

$\rule{90}3$

ii ) 7x² + 2√14x + 2.

→ 7x² + 2√14x + 2.

→ 7x² + √14x + √14x + 2.

→ √7x( √7x + √2 ) + √2 ( √7x + √2 ).

→ ( √7x + √2 )( √7x + √2 )

$\rule{90}3$

iii ) √2x² + 3x + √2.

→ √2x² + 3x + √2.

→ √2x² + 2x + x + √2.

→ √2x( x + √2 ) + 1 ( x + √2 )

→ ( √2x + 1 )( x + √2 )

$\rule{90}3$

iv ) x² + 3√3x + 6.

→ x² + 3√3x + 6.

→ x² + 2√3x + √3x + 6.

→ x( x + 2√3 ) + √3( x + 2√3 )

→ ( x + 2√3 )( x + √3 )

$\rule{90}3$

v ) 4√3x² + 5x - 2√3.

→ 4√3x² + 5x - 2√3.

→ 4√3x² + 8x - 3x - 2√3.

→ 4x( √3x + 2 ) - √3 ( √3x + 2 )

→ ( 4x - √3 )( √3x + 2 )

Answer 2

Step-by-step explanation:

SOLUTIONS :-

i ) 6√3x² - 47x + 5√3.

→ 6√3x² - 47x + 5√3.

→ 6√3x² - 45x - 2x + 5√3.

→ 3√3x( 2x - 5√3 ) - 1 ( 2x - 5√3

→ ( 3√3 - 1 )( 2x - 5√3 )

ii ) 7x² + 2√14x + 2.

→ 7x² + 2√14x + 2.

→ 7x² + √14x + √14x + 2.

→ √7x( √7x + √2 ) + √2 ( √7x + √2 ).

→ ( √7x + √2 )( √7x + √2 )

iii ) √2x² + 3x + √2.

→ √2x² + 3x + √2.

→ √2x² + 2x + x + √2.

→ √2x( x + √2 ) + 1 ( x + √2 )

→ ( √2x + 1 )( x + √2 )

iv ) x² + 3√3x + 6.

→ x² + 3√3x + 6.

→ x² + 2√3x + √3x + 6.

→ x( x + 2√3 ) + √3( x + 2√3 )

→ ( x + 2√3 )( x + √3 )

v ) 4√3x² + 5x - 2√3.

→ 4√3x² + 5x - 2√3.

→ 4√3x² + 8x - 3x - 2√3.

→ 4x( √3x + 2 ) - √3 ( √3x + 2 )

→ ( 4x - √3 )( √3x + 2 )