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Solving a Quadratic Equation by Factorization Method

Find two natu...

Question

Find two natural numbers which differ by 3 and whose squares have the sum 17.

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Solution

Let one natural number be and other.

Then according to question

Since, x being a natural number, so x cannot be negative.

Therefore,

When then even integer

Thus, two natural number be

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Q. 1. The sum of a number and its reciprocal is 17/4. find the number.
2. The sum of two numbers is 8 and the difference of their square is 16. find the numbers.
3. Find two consecutive natural numbers whose square have the sum 221.
4.There are three consecutive positive integers such that the sum of squares of first integer and product of second and third is 191. find those integer.

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