Question

if x(square) plus y(square) is 8.and the froduvt is . what are x and y?​

Answer 1

Given :-

• x² + y² = 8
• Product of x and y is 4 .( say )

To Find :-

• The value of x and y .

Answer :-

Here we are given that,

$\red{\longrightarrow}$ x² + y² = 8 .

And ,

$\red{\longrightarrow}$ xy = 4

$\red{\longrightarrow}$ y = 4/x

So that ,

$\red{\longrightarrow}$ x² + (4/x)² = 8

$\red{\longrightarrow}$ x² +16/x² = 8

$\red{\longrightarrow}$ x⁴ + 16 = 8x²

$\red{\longrightarrow}$ x⁴ - 8x² + 16 = 0

Assume k² = x⁴ and k = x²

$\red{\longrightarrow}$ k² - 8k + 16 = 0

$\red{\longrightarrow}$ k² -4k -4k +16 = 0

$\red{\longrightarrow}$ k(k-4) -4(k-4) = 0

$\red{\longrightarrow}$ (k-4)² = 0

$\red{\longrightarrow}$ k = 4

So ,

$\red{\longrightarrow}$ k = x²

$\red{\longrightarrow}$ 4 = x²

$\red{\longrightarrow}$ x = √4

$\red{\longrightarrow}$ x = ±2

Hence the required answer is ±2.

Answer 2

The values of x and y of the given function are; x = y = ±2

Roots of a Polynomial

We are given;

x² + y² = 8   -----(1)

Product of x and y = 4;

Thus; xy = 4

Now, making y the subject we have;

y = 4/x

Putting 4/x for y in eq 1 gives us;

x² + (4/x)² = 8  

x² + (16/x²) = 8

Multiply through by by x² to get;

x⁴ + 16 = 8x²

⇒ x⁴ - 8x² + 16 = 0

using online polynomial root calculator, we have x = ±2

Thus, y will also be ±2

Complete question is;

If x² + y² = 8 and the product of x and y is 4, what are x and y?

Read more about roots of a polynomial at; https://brainly.com/question/10702726