Question

if x=root 5+root3/root5-root3 and y=root5-root3/root5+root3 then find x²+y²​

Answer 1

given

$\sqrt{5} + \sqrt{3} \div \sqrt{5} - \sqrt{3}$

now rationalise it after rationalise the no will be x = 8+2 root 15÷2.

now given y =

$\sqrt{5} - \sqrt{3} \div \sqrt{5} + \sqrt{3}$

now also rationalise it after rationalise the no will be y= 8-2root15÷2.

now find x+y = 8.

now (x+y)^2= x^2+y^2+2.x.y.

after solve it the answer will be 62.

Answer 2

Answer:

Step-by-step explanation:

x =√5 +√3/√5 -√3

Rationalize the denominator and you will get

x = 8 + 2√15 /2

x = 2 ( 4 +√15 ) /2

x = 4+√15

Square on both sides

x² = 4² + √15² + 2( 4) (√15)

x² = 16+15 + 8√15

x²= 31 + 8√15

Since y = √5+√3/ √5 -√3

Rationalize the denominator and you will get

y = 5+3-2√15 /2

y = 8 -2√15 /2

y= 2 (4 -√15 ) /2

y = 4 - √15

square on both sides

y² = 4² + √15² - 2 (4)(√15)

y² = 16+15 - 8√15

y²= 31 - 8√15

THEN

x² +y² =31 +8√15 +31-8√15

         = 31 +31 = 62