The difference of squares of two natural numbers is 45

Asked by admin @ 02/08/2021 in Math viewed by 320 People

The difference of squares of two natural numbers is 45 . The square of the smaller number is 4 times the larger number.Then the numbers are ?

Answered by admin @ 02/08/2021

Solution:

Let the larger number be x and the smaller number be y.

It is given that,

The difference of square of two numbers is 45.

⇒ x² - y² = 45 .... (i)

Also, square of smaller number is four times the larger number.

⇒ y² = 4x

According to the question ;

x² - y² = 45

⇒ x² - 4x = 45 [Since, y² = 4x]

⇒ x² - 4x - 45 = 0

On splitting the middle term,

⇒ x² - (9 - 5)x - 45 = 0

⇒ x² - 9x + 5x - 45 = 0

⇒ x(x - 9) + 5(x - 9) = 0

⇒ (x - 9)(x + 5) = 0

⇒ x = 9 or x = - 5

Thus, by neglecting the negative value

We get the value of x = 9.

Substituting the value of x in (i)

⇒ x² - y² = 45

⇒ (9)² - y² = 45

⇒ 81 - y² = 45

⇒ y² = 81 - 45

⇒ y² = 36

⇒ y = ± √36

⇒ y = 6 [Neglecting negative value]

$\rule{300}{2}$

Therefore, the required numbers are-

x = 9
y = 6

Hence, the numbers are 9 and 6.

The difference of squares of two numbers is 45

Asked by admin @ 20/08/2021 in Math viewed by 324 persons

The difference of the squares of two numbers is 45 the square of the smallest number is 4 times the larger number determine the numbers.

The difference of squares of two numbers is 88

Asked by admin @ 13/08/2021 in Math viewed by 338 persons

The difference of squares of two numbers be 88. If the larger number is 5 less than twice the smaller Number then find two numbers.

The difference of squares of two numbers is 180

Asked by admin @ 10/08/2021 in Math viewed by 347 persons

The difference of squares of two numbers is 180.The square of the smaller number is 8 times the larger number. Find the two numbers.............(it's a sum of Quadratic Equations!!!!)

The difference of the squares of two numbers is 180

Asked by admin @ 05/08/2021 in Math viewed by 324 persons

The difference of squares of two numbers is 180.The square of the smaller number is 8 times the larger number. Find the two numbers.............(it's a sum of Quadratic Equations!!!!)

If the difference of two numbers is 8

Asked by admin @ 29/08/2021 in Math viewed by 372 persons

If the difference of two number is 8 and the difference of their squares is 160 then the numbers are

The difference between two whole number is 66

Asked by admin @ 25/08/2021 in Math viewed by 342 persons

The difference between two whole number is 66 . The ratio of the two numbers is 2 :5 .What are two numbers .

Sum of squares of n natural numbers formula

Asked by admin @ 24/08/2021 in Math viewed by 352 persons

Sum of squares of first square of n natural numbers formula

If alpha and beta are two different complex numbers

Asked by admin @ 20/08/2021 in Math viewed by 416 persons

Question 17 If α and β are different complex numbers with | β |= 1, then find | (β-α)/(1- αβ) |. Class X1 - Maths -Complex Numbers and Quadratic Equations …