Question

The sum of the squares of two consecutive real numbers is 85
Find the numbers​

Answer 1

Answer:

Let us assume the two consecutive natural numbers as a and a+1.

Given, a

2+(a+1) 2

=85

⇒a 2 +a 2+1+2a=85

⇒2a2+2a+1=85

⇒2a 2+2a−84=0

⇒a2+a−42=0

⇒a 2

+7a−6a−42=0

⇒a(a+7)−6(a+7)=0

⇒(a+7)=0 or (a−6)=0

⇒a=−7 or a=6

Considering positive number, a=6

The two consecutive numbers are a=6 and a+1=7.

Step-by-step explanation:

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