The difference between two positive integers | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the two positive integers be $x$ and $y$.Given that $x - y = 3$ and $x^2 + y^2 = 369$.We know the algebraic identity $(x - y)^2 = x^2 + y^2 -

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(B) Let the two positive integers be $x$ and $y$.Given that $x - y = 3$ and $x^2 + y^2 = 369$.We know the algebraic identity $(x - y)^2 = x^2 + y^2 - 2xy$.Substituting the known values: $3^2 = 369 - 2xy$,which gives $9 = 369 - 2xy$.Therefore,$2xy = 369 - 9 = 360$.We need to find the sum of the numbers,i.e.,$(x + y)$.Using the identity $(x + y)^2 = x^2 + y^2 + 2xy$,we substitute the values:$(x + y)^2 = 369 + 360 = 729$.Taking the square root on both sides,$x + y = \sqrt{729} = 27$ (since the integers are positive).Thus,the sum of the numbers is $27$.

The difference between two positive integers is $3$. If the sum of their squares is $369$,then the sum of the numbers is

Similar Questions

Rachita enters a shop to buy ice-creams,cookies,and pastries. She has to buy at least $9$ units of each. She buys more cookies than ice-creams and more pastries than cookies. She picks up a total of $32$ items. How many cookies does she buy?

If the sum of $4$ consecutive odd numbers is $184$,then find the largest number.

Find the unit digit in the product $(4387)^{245} \times (621)^{72}$.

When a number is divided by $56,$ the remainder is $29.$ If the same number is divided by $8,$ then the remainder will be:

$A$ two-digit number has $3$ as its unit's digit,and the sum of its digits is $\frac{1}{7}$ of the number itself. The number is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module