Question

Plss help me with this question

Answer 1

❥${\underline{\underline{\large{\mathbb{ANSWER:-}}}}}$

62

❥${\underline{\underline{\large{\mathbb{Step\:by\: step\: Explanation:-}}}}}$

★${\red{\underline{\bold{Given:-}}}}$

$x = \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} - \sqrt{3} }$

★${\red{\underline{\bold{To\:fnd:-}}}}$

${x}^{2} + \frac{1}{ {x}^{2} }$

★${\red{\underline{\bold{Solution:-}}}}$

${\sf{x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}}}$

★Now find the value of $\frac{1}{x}$

${\sf{\frac{1}{x}=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}}$

★Now find the value of x+1/x.

${\sf{\purple{x+\frac{1}{x}}}}$

${\sf{→\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}}}$+${\sf{\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}}$

${\sf{→\frac{(\sqrt{5}+\sqrt{3})^2+(\sqrt{5}-\sqrt{3})^2}{(\sqrt{5}-\sqrt{3})(\sqrt{5}-\sqrt{3})}}}$

${\sf{→\frac{5+2\sqrt{15}+3+5-2\sqrt{15}+3}{2}}}$

${\sf{→\frac{16}{2}}}$

$\large{\sf{\pink{→8}}}$

★Now find the value of x × 1/x.

${\sf{\green{x×\frac{1}{x}}}}$

${\sf{→\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}}}$×${\sf{\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}}}$

${\sf{\pink{→1}}}$

★Now find the value of ${x^2+\frac{1}{x^2}}$.

${\sf{\orange{x^2+\frac{1}{x^2}}}}$

† Apply a²+b² = (a+b)² -2ab †

${\sf{→(x+\frac{1}{x})^2-2.x.\frac{1}{x}}}$

${\sf{→(8)^2-2×1}}$

${\sf{→64-2}}$

${\sf{\pink{→62}}}$(Answer)

Answer 2

$\huge \mathfrak{Answer:-}$

$\implies$ 62

$\large\underline\mathrm{Given:-}$

$\implies$ (√5 + √3)/(√5 - √3)

$\large\underline\mathrm{To \: find}$

$\implies$ x² + 1/x²

$\large\underline\mathrm{Solution}$

$\implies$ x = (√5 + √3)/(√5 - √3)

$\large\underline\mathrm{The \: value \: of \: x \: - \: 1/x}$

$\implies$ x - 1/x

$\implies$ (√5 + √3)/(√5 - √3) + (√5 - √3)/(√5 + √3)

$\implies$ (√5 + √3)² + (√5 - √3)²/(√5 + √3)(√5 - √3)

$\implies$ 5 + 2√15 + 3 + - 2√15 + 3 / 2

$\implies$ 16/2

$\implies$ 8

Now,

the value of x × 1/x.

$\implies$ x × 1/x

$\implies$ (√5 + √3)/(√5 - √3) × (√5 - √3)/(√5 + √3)

$\implies$ 1

Now, the value of x² + 1/x².

Using formula a² + b² = (a + b)² - 2ab

$\implies$ (x² + 1/x)² - 2.x.1/x

$\implies$ (8)² - 2 × 1

$\implies$ 64 - 2

$\implies$ 62

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$