Question

If x=√5+1/√5-1, y=√5-1/√5+1, find the value of x²+xy+y²​

Answer 1

Answer: Step-by-step explanation: x=(√5+1)^2/4=(3+√5)/2. y=(√5-1)^2/4=(3-√5)/2. x²+xy+y²=(x+y)²-xy=9-1=8.

Answer 2

Answer:

99

Step-by-step explanation:

x= 5–2√6 (given)

yx=1 (given)

y=1/x

y=1/(5–2√6)

On rationalising,

y=1/(5–2√6) × (5+2√6)/(5+2√6)

y=(5+2√6)/[5²-(2√6)²]

y=(5+2√6)/(25–24)

y=(5+2√6)/1

y=5+2√6

We have found the value of y and x, now putting it in x²+xy+y²

=(5–2√6)²+(1)+(5+2√6)²

Expanding by using (a+b)²= a²+b²+2ab and (a-b)²=a²+b²-2ab

=[5²-2(5)(2√6)+(2√6)²]+1+[5²+2(5)(2√6)+(2√6)²]

=25–10√6+24+25+10√√6+24 (where -10√6 and 10√6 cancel out)

=25+25+24+24+1

=99

Hence the answer is 99