Question

if x=√5-2/√5+2 any y=√5+2/√5-2 find x²-y²​

Answer 1

Step-by-step explanation:

$x = \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2} \times \frac{ \sqrt{5} - 2} { \sqrt{5} - 2 } \\ = \frac{( \sqrt{5 } - 2) {}^{2} }{5 - 4} \\ = 5 + 4 - 2×2 \sqrt{5} \\ x {}^{2} = ( 9 - 4\sqrt{5} ) {}^{2} \\ = 81 + 16\times 5 - 2 \times 9 \times 4 \sqrt{5 } \\ = 161- 72\sqrt{5} \\ similarly \\ y = 9 + 4 \sqrt{5} \\ y {}^{2} = 161+ 72 \sqrt{5} \\ x {}^{2} - y {}^{2} = 161 - 72 \sqrt{5} - 161 - 72 \sqrt{5} \\ = - 144\sqrt{5} \\ answer$

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Answer 2

Step-by-step explanation:

x=

5

+2

5

−2

×

5

−2

5

−2

=

5−4

(

5

−2)

2

=5+4−2×2

5

x

2

=(9−4

5

)

2

=81+16×5−2×9×4

5

=161−72

5

similarly

y=9+4

5

y

2

=161+72

5

x

2

−y

2

=161−72

5

−161−72

5

=−144

5

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