Question

If x = 7+ 4√3 and xy = 1, then x² + y² is equal to​

Answer 1

THE CORRECT QUESTION IS

If x = 7+ 4√3 and xy = 1, then 1/x² + 1/y² is equal to​?

QUESTION FROM RD SHARMA CLASS 9  EDITION 2019  CHAPTER RATIONALISATION PAGE NUMBER 3.17 QUESTION 11

Solution

Given

x=7+4√3

xy=1

To Find

1/x²+1/y²

Explanation

x=7+4√3

xy=1

y=1/x

y=1/7+4√3

y=1×7-4√3/7+4√3×7-4√3  

y=7-4√3/(7)²-(4√3)² {(a+b)(a-b)=a²-b²}

y=7-4√3/49-48

y=7-4√3/1

y=7-4√3

1/x²+1/y²

1/1/y²+x²  {x=1/y, 1/y=x}

=y²+x²

=(7-4√3)²+(7+4√3)²  

=(7)²+(4√3)²-2×7×4√3+(7)²+(4√3)²-2×7×4√3

{a+b)²=a²+b²+2ab} {(a-b)²=a²+b²-2ab}

=49+48-56√3+49+48-56√3

=97+97

=194

Hence 1/x²+1/y²=194

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