Question

if x= √7-√5/√7+√5, y= √7+√5/√7-√5, then Find value of x^2+y^2
​

Answer 1

Answer:

ans: 142

Step-by-step explanation:

here x=1/y

x²+y²=(x+y)²-2xy

First find x+y

x+y=√7-√5/√7+√5 + √7+√5/√7-√5

=1/(√7-√5)(√7+√5) [(√7-√5)²+(√7+√5)²]

=1/7-5* ( 7+5-2*√7*√5+2*√7*√5+7+5)

=1/2*(24)=12

so x+y=12

===========================================

Now

x²+y²=(x+y)²-2xy

=12²-2*x*1/x   ( as y=1/x)

=144-2

=142

============================

Answer 2

Value of x^2+y^2 = 142.

Step-by-step explanation:

Given :

x= √7 - √5 ÷ √7 + √5

y= √7 + √5 ÷ √7 - √5

Let a and b be the 2 numbers,

• the squares of a and b are a² and b².
• The sum of the squares of a and b is a² + b².

We may want to reap a system the use of the acknowledged algebraic identity

(a+b)² = a² + b² + 2ab.

On subtracting 2ab from each the perimeters we are able to finish that

a² + b² = (a +b)² - 2ab.

Similarly, we also can say that,

a²+ b² = (a - b)² + 2ab.

now here

• x = 1/y

let's find

• x + y

=( √7 - √5 ÷ √7 + √5) + ( √7 + √5 ÷ √7 - √5 )

= 1 /(√7 - √5) (√7 + √5)( (√7 - √5 )² + (√7 + √5)²)

= 1/7-5 × (7+5-2 × √5 +2×√7×√5+7+5)

=½ × 24

= 12

now ,

x²+y²

= (x+y)²-2xy

=12² -2x × 1/x

= 144 -2

= 142.

hence , the value of x^2+y^2 = 142

(#SPJ2)