Question

Find two natural numbers whose sum is 50 and product 525.

Answer 1

Let the first natural number be $$x$$.

Then, the second natural number is $$(50 - x)$$.

According to the given condition: $$x(50 - x) = 525$$

$$50x - x^2 = 525$$

$$x^2 - 50x + 525 = 0$$ 

Splitting the middle term: $$x^2 - 35x - 15x + 525 = 0$$

$$x(x - 35) - 15(x - 35) = 0$$

$$(x - 35)(x - 15) = 0$$ 

$$x = 35 \quad \text{or} \quad x = 15$$ 

When $$x = 35$$, the other number is $$50 - 35 = 15$$. 

When $$x = 15$$, the other number is $$50 - 15 = 35$$.

Hence, the required natural numbers are 15 and 35.