The product of two numbers is 45 and the sum | vedclass

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

Question

(B) Let the two numbers be $x$ and $y$.Given that the product of the numbers is $xy = 45$ and the sum of their squares is $x^2 + y^2 = 106$.We know th

Vedclass · Accepted Answer

$5$ and $9$

Vedclass · Answer

(B) Let the two numbers be $x$ and $y$.Given that the product of the numbers is $xy = 45$ and the sum of their squares is $x^2 + y^2 = 106$.We know the identity $(x + y)^2 = x^2 + y^2 + 2xy$.Substituting the given values: $(x + y)^2 = 106 + 2(45) = 106 + 90 = 196$.Thus,$x + y = \sqrt{196} = 14$.We have $x + y = 14$ and $xy = 45$.These are the roots of the quadratic equation $t^2 - (x+y)t + xy = 0$,which is $t^2 - 14t + 45 = 0$.Factoring the equation: $(t - 9)(t - 5) = 0$.Therefore,the numbers are $5$ and $9$.

The product of two numbers is $45$ and the sum of their squares is $106$. The numbers are

Similar Questions

If a six-digit number $53a29b$ is divisible by $88$,then find the value of $a$ and $b$.

What is the number just more than $5000$ which is exactly divisible by $73$?

$A$ number,when divided by $296$,gives $75$ as the remainder. If the same number is divided by $37$,then the remainder will be:

$n$ is a whole number which when divided by $4$ gives the remainder $3$. The remainder when $2n$ is divided by $4$ is

$24$ is divided into two parts such that $7$ times the first part added to $5$ times the second part makes $146$. The first part is

Vedclass Test Series

Exam Paper Generator

Online Exam Module