Question

Two numbers are such that,the sum of the squares of two numbers is 113 and their product is 56.Twice the sum of the two number is​

Answer 1

Answer:

the sum of two number is 226

Answer 2

Given: Sum of squares of two numbers is 113 and their product is 56.

To Find

• Twice the sum of the two numbers?

Explanation

Let the two numbers be x and y

so as;

• x² + y² = 113
• xy = 56

Using Quantities,

$\\ \dag{\green{\boxed{\underline{\sf\large{ (x+y)^2 = x^2 + y^2 + 2xy }}}}}$

According to Question,

$\colon\implies{\tt{ (x+y)^2 = x^2 + y^2 + 2xy}} \\ \\ \\ \colon\implies{\tt{ (x+y)^2 = 113 + 2 \times 56 }} \\ \\ \\ \colon\implies{\tt{ (x+y)^2 = 113 + 112}} \\ \\ \\ \colon\implies{\tt{ (x+y)^2 = 225 }} \\ \\ \\ \colon\implies{\tt{ x+y = \sqrt{225} }} \\ \\ \\ \colon\implies{\tt{ x+y = 15 }}$

Therefore, Value of x + y = 15.

Now, we can find the Twice of the sum of the two numbers:-

$\colon\implies{\tt{ 2(x+y) }} \\ \\ \colon\implies{\tt{ 2(15) }} \\ \\ \colon\implies{\tt{ 2 \times 15 }} \\ \\ \colon\implies{\boxed{\tt\large\pink{ 30 }}}$

Hence,

• The Value of Twice the sum of the two number is 30 .