if X=4+√15/2 find the value of 16x²+1/x²
please it's urgent
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Answer:
màth vaule yesssßsssssssss
Answered by
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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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