Question

21. If a4 +1/a4= 322, find the value of a3-1/a3 please reply me with my answer​

Answer 1

$\huge\bold\star$$\mathrm\red{Question:-}$

$\mathrm{If\: a^{4} \:+1/a^{4}= 322, \:find\: the \:value \:of}$

$\mathrm{a^{3}-1/a^{3}}$,

$\huge\bold\star$$\mathrm\red{Given:-}$

$\implies \: {a}^{4} + \frac{1}{ {a}^{4} } = 322$

$\huge\bold\star$$\mathrm\red{Solution:-}$

$\mathrm{Adding\:2\:on\:both\:side}$,

$\longrightarrow \: {a}^{4} + \frac{1}{ {a}^{4} } + 2 = 322 + 2$

$\longrightarrow \:( {a}^{2} + \frac{1}{ {a}^{2} } )^{2} = 324$

$\longrightarrow \: \: ( {a}^{2} + \frac{1}{ {a}^{2} } ) = \sqrt{324}$

$\longrightarrow \: \: ( {a}^{2} + \frac{1}{ {a}^{2} } ) = 18$

$\mathrm{Subtracting\:2\:from\:both\:side}$

$\red \implies \: {a}^{2} + \frac{1}{ {a}^{2}} - 2 = 18 - 2$

$\red\implies \: {( {a} + \frac{1}{ {a} } })^{2} = 16$

$\red \implies \: a - \frac{1}{a} = 4$

$\mathrm{Now}$,

$\therefore \: ( {a}^{} - \frac{1}{a} )^{3}$

$\green\longrightarrow \: {a}^{3} - \frac{1}{ {a}^{3} } - 3 \times a \times \frac{1}{a} (a - \frac{1}{a} )$

$\green \longrightarrow \: {4}^{3} = {a}^{3} - \frac{1}{ {a}^{3} } - 3 \times 4$

$\green \longrightarrow \: {a}^{3} - \frac{1}{ {a}^{3} } = 64 + 72$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 76$

Hope it's helpful

Answer 2

Answer:

The above answer is correct dear................