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

$A$ 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:

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

If in a long division sum,the dividend is $380606$ and the successive remainders from the first to the last are $434, 125,$ and $413,$ then the divisor is:

$1 \frac{1}{4} + 1 \frac{5}{9} \times 1 \frac{5}{8} \div 6 \frac{1}{2} = ?$

$A$ number when divided by $357$ gives a remainder $37.$ By dividing the same number by $17,$ the remainder would be

Vedclass Test Series

Exam Paper Generator

Online Exam Module