Question

If x1 and x2 are the roots of 3 x square - 2 x minus 6 equal to zero then x square minus x square is equal to

Answer 1

Answer:

(x1)² - (x2)² = ( 2√76 ) / 9

Step-by-step explanation:

We are given

3x² - 2x - 6 = 0

By comparing with ax² + bx + c = 0

we get

a = 3   , b -2    , c = -6

Using quadric formula we get

x = (-b +-√(b² - 4ac) ) / 2a

Putting values we get

x = ( 2 +- √( 4 + 72) ) / 6

x = ( 2 +- √76 ) / 6

So

x = 2 + √76 ) / 6    or x = 2 - √76 ) / 6

Let

x1 = 2 + √76 ) / 6

x2 =  2 - √76 ) / 6

(x1)² - (x2)² = (2 + √76 ) / 6 )² -  (2 - √76 ) / 6 )²

Using identity

A² - B² = (A+B)(A-B) we get

(x1)² - (x2)² = [(2 + √76 ) / 6 ) + (2 - √76 ) / 6 )] [(2 + √76 ) / 6 )- (2 - √76 ) / 6 )]

(x1)² - (x2)² = [( 4 / 6 )] [(2√76 ) / 6 )]

(x1)² - (x2)² = [( 2 / 3 )] [(√76 ) / 3 )] = ( 2√76 ) / 9

Thus

(x1)² - (x2)² = ( 2√76 ) / 9