Question

the sum of two number is 6 and the sum of their squares is 28. Find the exact values of these numbers

Answer 1

Step-by-step explanation:

Given:-

• The sum of two numbers
• The sum of their squares

To Find:-

• The two numbers

Correct Question:-

The sum of two number is 6 and the sum of their squares is 26. Find the exact values of these numbers

Solution:-

Let two numbers be x and y

→x+y=6----(i)

→x²+y²=26

Now we have to find xy

So,

(x+y)²=x²+y²+2xy

(6)²=26+2xy

36=26+2xy

2xy=36-26

2xy=10

xy=5

Now we have to find the x-y

(x-y)²=(x+y)²-4xy

(x-y)²=(6)²-4(5)

(x-y)²=36-20

(x-y)²=16

x-y=4---(ii)

Adding (i) and (ii)

x+y=6

x-y=4

--------

2x=10

x=5

x+y=6

y=6-5=1

Required numbers=1 and 5

Answer 2

Correct Question -

The sum of two number is 6 and the sum of their squares is 26. Find the exact values of these numbers.

[ In the original question, the value of the sum of the squares is given wrong, it will be 26 not 28 ]

Solution -

• The sum of two numbers is 6

• The sum of their squares is 26.

We have to find the exact value of these two numbers.

Let us assume that they are a and b such that a,b € I

a,b € I a, b ≥ 1 . Either a or b or both can not be zero as no such solutión exists for that case.

As per the questión

a + b = 6

Squaring this

> a² + b² + 2ab = 36 [ a² + b² < 36 as 2ab ≥ 1 ]

Now , the sum of the squares is 28

So, a² + b² = 36

> 2ab + 26 = 36

> 2ab = 36 - 26 = 10

> ab = 5

There are two cases arising from ab = 5

• a = 1 and b = 5
• a = 5 and b = 1.

Both of these hold true here .

Answer - The exact values of the numbers satisfying the above property are tuples of (1,5) .

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