Question

the sum of the squares of two consecutive natural numbers is 421 find the numbers​

Answer 1

ello buddy!!

Let the two concecutive no.s be x and x+1

Sum of their squares is 421 (given)

ix² + (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

second number =x+1=14+1=15

Hence the 2 natural numbers are 14,15

Answer 2

Answer:

Step-by-step explanation:

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

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