Question

if x= root 2-1/root 2+1 and y= root 2+1/root2-1 then find the value of x2+5xy+y2

Answer 1

Answer:

your answer attached in the photo

Answer 2

Answer:

Step-by-step explanation:

The term "zeroes" refers to a polynomial's roots. The reason for this is that the roots are the x values where the function equals zero. Any expression with two or more algebraic terms is referred to as a polynomial. As the name suggests, a polynomial is an expression with numerous terms because poly means "many" and "nomial" means "terms."

Exponents, constants, and variables all make up a polynomial. To better comprehend a polynomial, let's examine three examples of them.

• $5n + 1$

• $a^{2} -5b + 6$

A polynomial's roots can be located using a variety of methods. Factoring is another technique that is used. A graph can also be used to locate a polynomial's roots. Here, we'll focus on a few methods that are frequently used. Additionally, it is crucial to remember the following:

• Terms with only positive integer exponents are known as polynomials.
• The operations of addition, subtraction, and multiplication are available to polynomials.
• An expression must be able to be written without being divided.

Given:

The values are

$x=\frac{\sqrt{2}-1 }{\sqrt{2} +1} ,y=\frac{\sqrt{2}+1 }{\sqrt{2}-1 }$

Find:

To find the value of $x^{2} +5xy+y^{2}$

Solution:

Given that

$x=\frac{\sqrt{2}-1 }{\sqrt{2} +1} ,y=\frac{\sqrt{2}+1 }{\sqrt{2}-1 }$

Sum of the terms $=x+y$

Product of the terms$=xy$

$x+y=\frac{(\sqrt{2}-1)^{2} +(\sqrt{2}+1)^{2} }{2-1}$

         $=2(2+1)$

         $=6$

$xy=(\frac{\sqrt{2}-1 }{\sqrt{2}+1 }) *(\frac{\sqrt{2}+1 }{\sqrt{2} -1} )$

$xy=1$

$x^{2} +5xy+y^{2} =(x+y)^{2} +3xy$

                      $=(6)^{2}+3(1)$

                      $=36+3$

                      $=39$

Hence the value of  $x^{2} +5xy+y^{2}$ is $39$

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