In this page quadratic equation practical solution2 we are going to see solution of practice question of the worksheet quadratic equation practical application.

Question 2:

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

Solution:

Let “x” be the larger number

Let “y” be the smaller number

x² – y² = 45   ------- (1)

y² = 4 x   ------- (2)

Now we are going to apply this value in the first equation

x² – 4 x = 45

x² – 4 x - 45 = 0

x² – 9 x  + 5 x - 45 = 0

x (x – 9) + 5 (x – 9) = 0

(x – 9) (x + 5) = 0

x – 9 = 0       x + 5 = 0

x = 9                x = - 5

Here positive 9 only admissible. From this we need to find the value of y for that we are going to apply this value in the second equation

y² = 4 (9)

y² = 36

y = 36

y = ± 6

Therefore the required numbers are 9 and 6.

Verification:

The difference of the squares of two positive numbers is 45

= 92 – 62

= 81- 36

= 45

The square of the smaller number is four times the larger number.

62 = 4 (9)

36  = 36

Question 6     Question 7     Question 8     Question 9     Question 10

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