Question

Find two consecutive numbers whose squares have the sum 85.

Answer 1

SOLUTION :  

Let the two consecutive numbers are x  & (x + 1)  

A.T.Q

x² + ( x + 1)² = 85

x² +( x² + 2x + 1) =  85  

[(a + b)² = a² + b² + 2ab]

x² + x² + 2x + 1 -  85  = 0

2x² + 2x - 84 = 0

2 ( x² + x - 42 ) = 0

x² + x - 42 = 0

x² + 7x - 6x - 42 = 0

[By middle term splitting method]

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

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

x + 7 = 0 or x - 6 = 0

x = -7 or x = 6

case 1 : If x = -7 , then (x + 1) = - 7 + 1 = - 6

case 2 : If x = 6 , then (x + 1) = 6 + 1 = 7

Hence, the two consecutive numbers are (6 , - 7) & (6 ,7) .

HOPE THIS ANSWER WILL HELP YOU …..

Answer 2

Answer:

Ans :

6,7 or -6, -7

Hint :

Let the natural numbers be x and x + 1. Then, by hypothesis, we have

x

2

+(x+1)

2

=85