Question

the product of two numbers is 45 and their differnce is 4. the sum square of two numbers is

Answer 1

Hey friend, Harish here.

Here is your answer:

Let the two number be x & y.

Given that,

1)x × y = 45 

2)x - y = 4

To find,

x² + y²

Solution,

We know that, 

( x -y) = 4.   

Now take square on both sides.

Then, 

→ ( x - y) ² = 4²

→ x² + y² - 2xy = 16.

→ x² + y² = 16 + 2xy 

Now substitute value of xy.

Then,

→ x² + y² = 16 + 2(45)

                = 16 + 90
 
                = 106.

Therefore value of the sum of squares of the numbers is 106.
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Hope my answer is helpful to you.

Answer 2

Let the largest number be x and the smallest be y
xy = 45
x - y = 4
(x-y)² = 4² = 16
x² + y² - 2xy = 16
x² + y² - 2 × 45 = 16
x² + y² - 90 = 16
x² + y² = 16 + 90 = 106

∴ The sum square of two numbers is 106


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