Question

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.

Answer 1

Let two no/s be x(greater) and y(smaller)
Then acc to ques,
   x² - y² = 45          ...(1)
Also, 
         y² = 4x          ...(2)
From 1 and 2
Substituting 2 in 1
We get, 
     x² - y² = 45
     x² - 4x = 45
⇒ x² - 4x - 45
⇒ x² - 9x + 5x  -45
⇒ x(x - 9) + 5(x - 9)
⇒ (x+5)(x-9)
⇒ Then x = -5,9

If x = -5
   y² = 4(-5)
   y² = -20
   y  =  √-20       which is not applicable here
Negative neglected  

If x = 9
   y² = 4(9)
   y² = 36
    y = √36
    y = 6

Hence the no/s are 9 and 6

:)(: Hope This Helps !!! :)(:

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the larger number be x.

Then,

Square of the smaller number = 4x

Square of the larger number = x²

Difference of the squares of number = 45

According to the Question,

⇒ x² - 4x = 45

⇒ x² - 4x - 45 = 0

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, - 5.

When x = 9,

Square of smaller number = 4x = 4 × 9 = 36

Smaller number = ± 6

Thus, the numbers are 9 and 6 or 9 and - 6.

When x = - 5

Square of smaller number = 4x = 4 × (- 5) = - 20

Hence, the numbers are 9 and 6 or 9 and - 6.