Question

b) The sum of two numbers is 9 and their product is 20. Find the sum of their
i) squares
ii)cubes
​

Answer 1

• square of the numbers = 41
• cube of the numbers = 189

Step-by-step explanation:

Given :-

• The sum of two numbers is 9 .
• and their product is 20.

To find :-

Find the sum of their –

1. squares
2. cubes

Solution :-

• Let first number = x
• and second number = y

sum of numbers = 9 .

So, x + y = 9 ..........eq.(1)

Product of numbers = 20 .

So, x × y = 20 .........eq.(2)

From eq.(1)

x + y = 9

x = 9 – y ..........eq.(3)

Put the value of x = 9 – y from eq.(3) into eq.(2) we get :-

⟼ ( 9 – y ) × y = 20

⟼ 9y – y² = 20

⟼ – y² + 9y = 20

⟼ – y² + 9y – 20 = 0

(multiply by (–) we get )

⟼ y² – 9y + 20 = 0

( splitting the middle term )

⟼ y² – ( 5 + 4 )y + 20 = 0

⟼ y² – 5y – 4y + 20 = 0

⟼ y( y – 5 ) – 4( y – 5 ) = 0

⟼ ( y – 5 ) ( y – 4 ) = 0

⟼ y – 5 = 0 or y – 4 = 0

⟼ y = 5 or y = 4

So, Second number can be 5 or 4 .

When y = 5 then value of x =

Put the value of y = 5 in eq.(3)

⟼ x = 9 – y

⟼ x = 9 – 5

⟼ x = 4

When y = 4 then value of x =

Put the value of y = 4 in eq.(3) we get

⟼ x = 9 – y

⟼ x = 9 – 4

⟼ x = 5

So, the first number can be 4 or 5

Hence, the numbers can be 45 or 54.

Now, the sum of their Squares =

⟼ ( 5 )² + ( 4 )²

⟼ 25 + 16

⟼ 41

The sum of their Cubes =

⟼ ( 5 )³ + ( 4 )³

⟼ 125 + 64

⟼ 189