Question

if x=2+√3 & y=2-√3, then 1/x² -1/y² is _____​

Answer 1

Answer:

x=2+√3

x^2= (2+√3)^2

= 2^2+2×2×√3+√3^2

= 4+4√3+3

= 7+4√3

y=2-√3

y^2= (2-√3)^2

= 4-4√3+3

= 7-4√3

therefore 1/x^2-1/y^2

= 1/(7+4√3)-1/(7-4√3)

= (7-4√3/49-48)-(7+4√3/49-48)

= 7-4√3-(7+4√3)

= 7-4√3-7-4√3

= -8√3

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