Question

Factorize :- x2(square)-bx+5

Answer 1

Answer:

( x - ( b/2) +√(b²- 20)/√5 ) ( x -b/2-√(b²-20)/√5 )

Step-by-step explanation:

To find---> Factors of x² - bx + 5

Solution---->

x² - bx + 5

Multiplying 2 and dividing by 2 in second term , we get,

= ( x )² - 2 ( b / 2 ) ( x ) + 5

= ( x )² - 2 ( b / 2 ) ( x ) + b² / 4 - b² / 4 + 5

= ( x )² - 2 ( b / 2 ) ( x ) + ( b / 2 )² - ( b²/4 - 5 )

We have an identity , ( a - b )² = a² + b² - 2ab, applying it here , we get,

= { x - ( b / 2 ) }² - ( b² - 20 ) / 5

= { x - ( b/2 ) }² - ( √(b² - 20 ) / √5 )²

We have an identity a² - b² = ( a + b ) ( a - b ),applying it here , we get,

= { x - ( b / 2 ) + (√(b² - 20 ) / √5 }

{ x - b/2 - √(b²-20) / √5 }