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

Here positive 6 only admissible.

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

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- Back to worksheet
- More practice problems
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- Factoring Worksheets
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- Relationship Between Coefficients and roots
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- Roots of Polynomial of Degree4
- Roots of Polynomial of Degree5

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”