Question

3. Find two
4. Find two consecutive positive integers, sum of whose squares is 365.
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Answer 1

Answer:

13*13+14*14=365 two consecutive positive integer

Answer 2

Given :-

Sum of whose squares = 365

To Find :-

The first integer.

The second integer.

Solution :-

Let the two consecutive positive integers be x and x + 1.

Given that,

Sum of whose squares = 365

According to the question,

x² + (x + 1)² = 365

Opening brackets,

x² + x² + 1 + 2x = 365

Transposing 1,

2x² + 2x - 365 - 1

2x² + 2x - 364 = 0

Transposing 2,

x² + x - 364/2

x² + x - 182 = 0

x² + 14x – 13x – 182 = 0

Now,

x(x + 14) - 13(x + 14) = 0

(x + 14)(x - 13) = 0

x = - 14 or x = 13

Since the integers cannot be negative,

x = 13

Finding the other integer,

x + 1 = 13 + 1

= 14

Therefore, two consecutive positive integers are 13 and 14.