Question

if X = an and Y = a+b, where a= 5+√5, b=5-√5 then find whether X and Y are rational irrational​

Answer 1

Answer:

See the attachment. It can help you

Step-by-step explanation:

X is an irrational

Y is a rational

Answer 2

Question:-

if X = ab and Y = a+b, where a= 5+√5, b=5-√5 then find whether X and Y are rational irrational

Solution:-

Now first we have to find the value of X

X= a×b

a=5+√5, b=5-√5

X= 5+√5× 5-√5

It is in the form of (a+b) (a-b) = a²-b²

X= 5+√5× 5-√5

X= (5)²-(√5)²

X= 25-5

X= 20

So, X is a rational number

Now Find the value of Y

Y= a+b

a=5+√5, b=5-√5

Y= 5+√5+ 5-√5

Here +√5 and -√5 will be cancelled

Then we get

Y= 5+5

Y= 10

So, Y also a Rational number

Answer:-

X and Y are rational numbers

More Information:-

(a+b) ²= a²+b²+2ab

(a-b) ² = a²+b²-2ab

a²-b²=(a+b) (a-b)

(a+b) ²-(a-b) ²=4ab

(a+b) ²+(a-b) ²=2(a²+b²)

a²+b²=(a+b) ²-2ab

(a+b) ³=a³+3a²b+3ab²+b³

(a-b) ³=a³-b³-3ab(a-b)

a³+b³=(a+b) (a²-ab+b²)

a³-b³=(a+b) (a²+ab+b²)

(a+b+c) ²=a²+b²+c²+2ab+2bc+2ca

a³+b³+c³-3abc=(a+b+c) (a²+b²+c²-ab-bc-ca)