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