x+1x = a হলে x2+1x2 এর মান কত ?

Question

Shohan

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2025-01-04 04:42

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x + 1x2 = 7 হলে x3 - 1x3= ?

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x+1x=3 হলে, x4-1x2 = ?

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2x +2x= 3 হলে x2+1x2=?

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Shohan · Accepted Answer · 2024-12-14T13:31:11+06:00

Shohan

$\sqrt{x} + \frac{1}{\sqrt{x}} = a$ বা, ${(\sqrt{x} + \frac{1}{\sqrt{x}})}^{2} = a^{2}$

বা, ${(\sqrt{x})}^{2} + 2 . \sqrt{x} . \frac{1}{\sqrt{x}} + {(\frac{1}{\sqrt{x}})}^{2} = a^{2}$

বা, $x + \frac{1}{x} + 2 = a^{2}$

বা, ${(x + \frac{1}{x})}^{2} = {(a^{2} - 2)}^{2}$ [বর্গ করে]

বা, $x^{2} + 2 . x . \frac{1}{x} + \frac{1}{x^{2}} = a^{4} - 4 a^{2} + 4$

বা, $x^{2} + \frac{1}{x^{2}} + 2 = a^{4} - 4 a^{2} + 4$

∴ $x^{2} + \frac{1}{x^{2}} = a^{4} - 4 a^{2} + 4 - 2 = a^{4} - 4 a^{2} + 2$

4 views Answered 2024-12-14 13:31