Question

Sum of squares of the two consecutive natural number is 421

Answer 1

Let the 2 concecutive no.s be x and x+1
Sum of their squares is 421 (given)
i.e., x² + (x+1)² = 421
x²+x²+2x+1=421
2x²+2x=421-1
2(x²+x)=420
x²+x=210
x²+x-210=0
x²+15x-14x+210=0
x(x+15) -14(x+15)
(x+15)(x-14)=0
x+15=0    or     x-14=9
x= -15  or  x=14
-15 is not a natural number
So, First number  x=14
 and second number = x+1 = 14+1 =15
Hence the 2 natural numbers are 14,15

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the first natural number be x.

Second consecutive natural number be be x + 1.

According to the Question,

⇒ x² + (x + 1)² = 421

⇒ x² + x² + 2x + 1 = 421

⇒ x² + x - 210 = 0

⇒ x² + 15x - 14x - 210 = 0

⇒ x(x + 15) - 14(x + 15) = 0

⇒ (x + 15) (x - 14)

⇒ x + 15 = 0 or x - 14 = 0

⇒ x = - 15 or 14 (Rejecting negative value)

First Number = x = 14

Second Number = x + 1 = 14 + 1 = 15.