Question

if x^2 +1/x^2=14 then find the value of x+1/x​

Answer 1

x²+1/x²=14

x²+1/x²=14(x+1/x)²-2.x.1/x=14

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots(x+1/x)=4

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots(x+1/x)=4then

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots(x+1/x)=4thenx³+1/x³-3.x.1/x(x+1/x)

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots(x+1/x)=4thenx³+1/x³-3.x.1/x(x+1/x)(x+1/x)³-3(x+1/x)

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots(x+1/x)=4thenx³+1/x³-3.x.1/x(x+1/x)(x+1/x)³-3(x+1/x)(4)³-3(4)

x²+1/x²=14(x+1/x)²-2.x.1/x=14(x+1/x)²-2=14(x+1/x)²=16Take off the square roots(x+1/x)=4thenx³+1/x³-3.x.1/x(x+1/x)(x+1/x)³-3(x+1/x)(4)³-3(4)64-12

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Hope it helps you!!!

Answer 2

$\\ \large\sf\underline{ \underline{ \red{given : }}}$

$\sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 14 }$

$\\ \\ \large\sf\underline{ \underline{ \red{to \: find : }}}$

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

$\\ \\ \large\sf\underline{ \underline{ \red{solution : }}}$

$\boxed{ \bf{(a + {b)}^{2} = {a}^{2} + {b}^{2} + 2ab }}$

Here ,

• a = x

• b = 1/x

Putting values , we get..

$\\ \implies\sf \: (x + { \frac{1}{x}) }^{2} = \underline{{x}^{2} + { (\frac{1}{x}) }^{2} } + 2( \cancel{x})( \frac{1}{ \cancel x } ) \\ \\ \\ \implies \sf \:( x + { \frac{1}{x} )}^{2} = 14 + 2 \\ \\ \\ \implies\sf{(x + { \frac{1}{x} )}^{2} } = 16 \\ \\ \\ \implies\sf \: x + \frac{1}{x} = \sqrt{16} \\ \\ \\ \implies \underline{\boxed{ \rm{ \green{x + \frac{1}{x} = 4}}}}$

More identities :-

• ( a - b )² = a² + b² - 2ab

• (a+b)(a-b) = a² - b²

• (a+x)(a+y) = a² + (x+y)a + xy