Question

Find two consective positive integers ; sum of whose squares is 365

Answer 1

Answer:

Two consective positive integers ; sum of whose squares is 365 are 13,14.

Step-by-step explanation:

let the numbers =x,x+1

According to question,

→x²+(x+1)²=365

→x²+x²+1+2x=365

→2x²+2x+1=365

→2x²+2x+1-365=0

→2x²+2x-364=0

→x²+x-182=0

→x²+14x-13x-182=0

→x(x+14)-13(x+14)=0

→x+14)(x-13)=0

If,

If,x+14=0

If,x+14=0then,

If,x+14=0then,x=-14(It is not a positive integer so we will neglect it)

If,

If,x-13=0

If,x-13=0then,

If,x-13=0then,x=13(It is a positive integer)

So, two consective positive integers ; sum of whose squares is 365 are 13,14.

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Answer 2

Two consective positive integers ; sum of whose squares is 365 are 13,14.

Step-by-step explanation:

let the numbers =x,x+1

According to question,

→x²+(x+1)²=365

→x²+x²+1+2x=365

→2x²+2x+1=365

→2x²+2x+1-365=0

→2x²+2x-364=0

→x²+x-182=0

→x²+14x-13x-182=0

→x(x+14)-13(x+14)=0

→x+14)(x-13)=0

If,

If,x+14=0

If,x+14=0then,

If,x+14=0then,x=-14(It is not a positive integer so we will neglect it)

If,

If,x-13=0

If,x-13=0then,

If,x-13=0then,x=13(It is a positive integer)

So, two consective positive integers ; sum of whose squares is 365 are 13and14