Question

X square+5x-a square-a+6=0

Answer 1

Answer:

x = - ( a + 3 ) or x = ( a - 2 )

Step-by-step explanation:

To find--->

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x² + 5x - a² - a + 6 = 0

Solution--->

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x² + 5x - ( a² + a - 6 )= 0

Now taking only 5

adding and subtracting 'a' to 5

5 = a - a + 5

Writing (-5) as +3 and 2

= (a + 3 ) - ( a - 2 )

Now taking ( a² + a - 6 )

We factroize it by splitting the middle

term

We break 6 in to two parts such that whose difference is one which are 3 and 2

a² + a - 6 = a² + ( 3 - 2 ) a - 6

= a² + 3 a - 2 a - 6

= a ( a + 3 ) - 2 ( a + 3 )

= ( a + 3 ) ( a - 2 )

Now

x² + 5 x - a² - a + 6 =0

=> x² + ( 5 ) x - ( a² + a - 6 ) = 0

Now putting values of 5 and (a² +a - 6)

=> x² + {(a+3)- ( a -2)} x -(a +3 ) (a - 2)= 0

=> x² +(a +3 )x - (a- 2)x -( a +3) ( a - 2)= 0

=> x {x +(a + 3)} - (a-2) {x + ( a +3 )}= 0

=> {x + ( a + 3 ) } { x - ( a - 2 ) } = 0

If x + ( a + 3 ) = 0

x = - ( a + 3 )

If x - ( a - 2 ) = 0

x = ( a - 2 )