The difference of the squares of two positive numbers is 45. The squar

1.	The difference of the squares of two positive numbers is 45. The square of thesmaller number is four times the larger number. Find the numbers
Answer» Answer: 9 and 6 are the NUMBERS Given : The DIFFERENCE of the squares of two POSITIVE numbers is 45 The square of the smaller number is four TIMES the larger number To find : Numbers Solution : Let the larger number be x Let the smaller number be y Given that , The differences of the squares of two positive numbers is 45 then , x² + y² = 45 is eq (1) And also , the square of the smaller number is four times the larger number then y² = 4x is eq(2) According to Question, From eq (1) and eq (2) we get , 》x² + y² = 45 + y² = 4x 》x² - 4x = 45 》x² - 4x - 45 = 0 》x² - (9 - 5) x - 45 = 0 Now by using factorization method we get, 》x² - 9x + 5x - 45 = 0 》x(x - 9) + 5(x - 9) = 0 》(x - 9) (x + 5) = 0 》x - 9 = 0 or x + 5 = 0 》x = - 9 , x = - 5 》x = 9 Now , putting the value in eq (2) we get, 》y² = 4x 》y² = 4(9) 》y² = 36 》 y = √36 》y = 6 Hence , 9 and 6 are the numbers

The difference of the squares of two positive numbers is 45. The square of thesmaller number is four times the larger number. Find the numbers

Answer»

Answer:

9 and 6 are the NUMBERS

Given :

The DIFFERENCE of the squares of two POSITIVE numbers is 45
The square of the smaller number is four TIMES the larger number

To find :

Numbers

Solution :

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

Given that , The differences of the squares of two positive numbers is 45 then ,

x² + y² = 45 is eq (1)

And also , the square of the smaller number is four times the larger number then

y² = 4x is eq(2)

According to Question, From eq (1) and eq (2) we get ,

》x² + y² = 45 + y² = 4x

》x² - 4x = 45

》x² - 4x - 45 = 0

》x² - (9 - 5) x - 45 = 0

Now by using factorization method we get,

》x² - 9x + 5x - 45 = 0

》x(x - 9) + 5(x - 9) = 0

》(x - 9) (x + 5) = 0

》x - 9 = 0 or x + 5 = 0

》x = - 9 , x = - 5

》x = 9

Now , putting the value in eq (2) we get,

》y² = 4x

》y² = 4(9)

》y² = 36

》 y = √36

》y = 6

Hence , 9 and 6 are the numbers