Math, asked by shahabulrahman02032, 16 days ago

(4-√15)square2 plz solv​

Answers

Answered by visalkumar161104
0

Step-by-step explanation:

Given,

x=4-\sqrt{15}x=4−

15

\implies \frac{1}{x}=\frac{1}{4-\sqrt{15}}⟹

x

1

=

4−

15

1

=\frac{1}{4-\sqrt{15}}\times \frac{4+\sqrt{15}}{4+\sqrt{15}}=

4−

15

1

×

4+

15

4+

15

=\frac{4+\sqrt{15}}{(4)^2-(\sqrt{15})^2}=

(4)

2

−(

15

)

2

4+

15

=\frac{4+\sqrt{15}}{16-15}=

16−15

4+

15

=\frac{4+\sqrt{15}}{1}=

1

4+

15

=4+\sqrt{15}=4+

15

Thus,

x^2+\frac{1}{x^2}=(4-\sqrt{15})^2+(4+\sqrt{15})^2x

2

+

x

2

1

=(4−

15

)

2

+(4+

15

)

2

=16+15-20\sqrt{15}+16+15+20\sqrt{15}=16+15−20

15

+16+15+20

15

( Because, (a±b)² = a² ± 2ab + b² )

=62=62

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