Question

if 5+√x=y+√2 , then y-x =?​

Answer 1

Answer:

1

If x = 5-2√6 and yx =1,then what is the value of x² + xy + y²?

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Akash Bora

Answered September 21, 2019

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