Question

the sum of squares of two nos. is 90 and squares of their difference is 36.find the product of the two numbers.

Answer 1

9×3=27 as 3×3+9×9=90
and the difference between 9-3 is 6 and it's square is 36

Answer 2

Answer:

27

Step-by-step explanation:

Given : The sum of squares of two nos. is 90 and squares of their difference is 36.

To Find : Find the product of the two numbers.

Solution:

Let the numbers are x and y,

We are given that the sum of squares of two numbers is 90

$\Rightarrow x^2+y^2=90$  ---1

Now we are given that the square of difference between the two numbers is 36,

$\Rightarrow (x-y)^2=36$

Property : $(a-b)^2=a^2+b^2-2ab$

So, $\Rightarrow x^2+y^2-2xy=36$

Using 1

So, $\Rightarrow 90-2xy=36$

$\Rightarrow 90-36=2xy$

$\Rightarrow 54=2xy$

$\Rightarrow \frac{54}{2}=xy$

$\Rightarrow 27=xy$

Hence the product of the two numbers is 27.