Question

if (x+1/x=7,find the value of the following : x4+1/x4​

Answer 1

Answer:

$\large{\underline{\boxed{\sf 2207}}}$

Step-by-step explanation:

Given that ;

$\tt x + \dfrac{1}{x} = 7$

On squaring both sides,

$\implies \tt \left (x + \frac{1}{x} \right ) ^{2} = (7) {}^{2} \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 \: . \:x \: . \: \frac{1}{x} = 49 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 49 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } = 49 - 2 \\ \\ \implies \tt {x}^{2} + \frac{1}{ {x}^{2} } = 47$

Again, on squaring both sides,

$\implies \tt \left({x}^{2} + \frac{1}{ {x}^{2} } \right)^{2} = (47) {}^{2} \\ \\ \implies \tt ({x}^{2} ) {}^{2} + \frac{1}{ ({x}^{2} ) {}^{2} } + 2 \:. \: {x}^{2} \: \: \frac{1}{ {x}^{2} } = 2209 \\ \\ \implies \tt {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 2209 \\ \\ \implies \tt {x}^{4} + \frac{1}{ {x}^{4} } = 2209 - 2 \\ \\ \red{\boxed{ \therefore \: \bf {x}^{4} + \frac{1}{ {x}^{4} } = 2207}}$

Answer 2

Answer:

$\huge{\red{\boxed{\boxed{\green{\sf{x^{4}+\frac{1}{x^{4}}=2207}}}}}}$

Step-by-step explanation:

$\huge{\red{\boxed{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}}$

${ \: \: \: \: \: \pink {given}} \\ {\boxed {\green{ x + \frac{1}{x} = 7}}} \\ \\ \: \: \: { \blue {to\: find}} \\ {\boxed{ \red{ {x}^{4} + \frac{1}{ {x}^{4} } = ?}}}$

$\: \: \: \: \: \: \: use \: formula \: \\ { \green{ \boxed{ ({x + y})^{2} = {x}^{2} + {y}^{2} + 2xy }}} \\ x + \frac{ 1 }{x} = 7 \\ squaring \: both \: side \\ ( {x + \frac{1}{x} })^{2} = {7}^{2} \\ {x}^{2} + ({ \frac{1}{x} })^{2} + 2 \times x \times \frac{1}{ x} = 49 \\ {x}^{2} +( { \frac{1}{x} })^{2} = 49 - 2 \\ {x}^{2} + ( { \frac{1}{x} })^{2} = 47 - - - - - (1) \\ \\ again \: both \: side \: squaring \: \\ ( { {x}^{2})^{2} + ({ \frac{1}{x^{2} } } )}^{2} = {47}^{2} \\ {x}^{4} + \frac{1}{x ^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 2209 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 2209 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 2209 - 2 \\ ( {x}^{4} + \frac{1}{ {x}^{4} } ) = 2207$

$\huge{\red{\boxed{\boxed{\green{\sf{x^{4}+\frac{1}{x^{4}}=2207}}}}}}$

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