Question

Represent the following situations in the form of quadratic equations :
Find two consecutive positive integrs, Sum of whose square is 85.​

Answer 1

Answer:

Step-by-step explanation:

Let the two consecutive integers be X and X+1

Now according to the question

x²+(X+1)²=85

Or x²+x²+2(X)(1)+(1)²=85

Or 2x²+2x+1=85

Or 2x²+2x+1-85=0

Or 2x²+2x-84=0

Or 2x²+(14-12)x-84=0 (by middle term splitting)

Or 2x²+14x-12x-84=0

Or 2x(x+7)-12(X+7)=0

Or (2x-12)(X+7)=0

Therefore either 2x-12=0 or X+7=0

Therefore X= 6 or X= 7

Therefore the two consecutive integers are 6 and 7