Question

4 and 81 are sq numbers with a sum of 85 . find 2 different sq. number with a sum of 85​

Answer 1

Step-by-step explanation:

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

⇒2a

2

+2a+1=85

⇒2a

2

+2a−84=0

⇒a

2

+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 (because they are natural numbers), a=6

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