Question

lf x= 2+√2and y =2-√2 find the value of x square +y square​

Answer 1

Step-by-step explanation:

Given:-

x= 2+√2and y =2-√2

To find:-

Find the value of x^2 +y^2 ?

Solution:-

Given that

x= 2+√2and y =2-√2

x^2 = (2+√2)^2

This is in the form of (a+b)^2

Where, a=2 and b=√2

We know that

(a+b)^2 =a^2+2ab+b^2

=>x^2 =2^2+2(2)(√2)+(√2)^2

=>x^2=4+4√2+2

x^2=6+4√2------(1)

And y^2 = (2-√2)^2

This is in the form of (a-b)^2

Where, a= 2 and b = √2

We know that

(a-b)^2 = a^2-2ab+b^2

y^2=2^2-2(2)(√2)+(√2)^2

=>y^2 = 4-4√2+2

y^2=6-4√2---------(2)

Now the value of x^2+y^2

From (1)&(2)

=>x^2+y^2

=>6+4√2+6-4√2

=>6+6

=>12

x^2+y^2 = 12

Answer:-

The value of x^2+y^2 for the given problem is 12

Used formulae:-

• (a+b)^2 =a^2+2ab+b^2

• (a-b)^2 = a^2-2ab+b^2