Question

if x=1/3-2√2 and y= 1/3+2√2 then find x+y + xy

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Answer 1

Hope this helps you ☺

Answer 2

CONCEPT:

Binomial expansion is an algebraic expression for the algebraic expansion of a binomial's powers. When a polynomial (x + y)ⁿ is expanded using the binomial method, it results in a sum of terms with the formula an x + b y + c, where b and c are non-negative integers and the coefficient an is a positive integer that depends on the values of n and b.

a²-b²=(a+b)(a-b)

(a+b)²=a²+2ab+b²

(a-b)²=a²-2ab+b²

(a-b)³=a³-b³-3a²b+3ab²

(a+b)³=a³+b³+3a²b+3ab²

Given:

x=1/3-2√2 and y= 1/3+2√2

Find:

x+y + xy=?

Solution:

x=1/3-2√2 and y= 1/3+2√2

x+y + xy=1/3-2√2+1/3+2√2+(1/3+2√2)(1/3-2√2)

             =2/3+(1/9-8)

             =5/9-8

             =-67/9

Therefore, x+y + xy=-67/9

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