Question

find the two consecutive numbers whose squares have the sum 85 {by quadratic equation formula) plzzz fast tomorrrow i need to submitthe sum of two numbers is 15 if their reciprocals is 3/10 find the two number using quadratic formula

Answer 1

Hi ,

1 ) Let x , ( x + 1 ) are two consecutive numbers

x² + ( x + 1 )² = 85

x² + x² + 2x + 1 - 85 = 0

2x² + 2x - 84 = 0

2 ( x² + x - 42 ) = 0

x² + x - 42 = 0

x² + 7x - 6x - 42 = 0

x( x + 7 ) - 6(x + 7 ) = 0

( x + 7 )( x - 6 ) = 0

x + 7 = 0 or x - 6 = 0

x = -7 or x = 6

Therefore ,

i ) if x = -7 , x + 1 = - 7 + 1 = -6

( - 7 , - 6 )

ii ) if x = 6 , x + 1 = 6 + 1 = 7

( 6 , 7 )

2 ) Sum of the two numbers = 15 ,

first number = x ,

second number = 15 - x

1/x + 1/( 15 - x ) = 3/10

( 15 - x + x )/ [ x( 15 - x )] = 3/10

15/( 15x - x² ) = 3/10

5/( 15x - x² ) = 1/10

50 = 15x - x²

x² - 15x + 50 = 0

x² - 10x - 5x + 50 = 0

x( x - 10 ) - 5( x - 10 ) = 0

( x - 10)( x - 5 ) = 0

x - 10 = 0 or x - 5 = 0

x = 10 or x = 5

Therefore ,

Required numbers are ,

1 ) if x = 10 ,

15 - x = 15 - 10 = 5

( 10 , 5 )

I hope this helps you.

: )