Question

if (x-1/x)² = x² + a + 1/x² then a = ?​

Answer 1

Step-by-step explanation:

As per the provided information in the given question, we have been provided that,

• $\rm {{ \Bigg \{ x - \dfrac{1}{x} \Bigg \}}^{2} = x^2 + a + \dfrac{1}{x^2} }$

We have been asked to calculate the value of a.

So, here we'll have to use algebraic identities in order to tackle this question. We know that,

⠀⠀⠀⠀⠀⠀⠀★ (a ― b)² = a² + b² — 2ab

Henceforth, using this identity let's simplify the LHS.

$\dashrightarrow \quad \rm { (x)^2 + {\Bigg (\dfrac{1}{x}\Bigg )}^2 - 2\Bigg \{ x\Bigg (\dfrac{1}{x}\Bigg ) \Bigg \} = x^2 + a + \dfrac{1}{x^2} }$

$\dashrightarrow \quad \rm { x^2 + \dfrac{1}{x^2} - 2\Bigg \{ 1 \Bigg \} = x^2 + a + \dfrac{1}{x^2} }$

$\dashrightarrow \quad \rm { x^2 + \dfrac{1}{x^2} - 2= x^2 + a + \dfrac{1}{x^2} }$

Transposing like terms.

$\dashrightarrow \quad \rm { \cancel{x^2+ \dfrac{1}{x^2}} - 2\cancel{ - \dfrac{1}{x^2} - x^2} = a }$

$\dashrightarrow \quad \underline{\boxed{ \bf {-2 = a } }}$

∴ The value of a is ― 2.

$\rule{200}2$

Answer 2

Given that ,

$↪ \: \large{\rm[x - \frac{1}{x} ] { }^{2} \: = \: {x}^{2} + a + \frac{1}{ {x}^{2} } }$

To find ;

value of a

$\underline{ \pink{ \bf SOLUTION }} :$

we can solve this sum by using,

(a - b)² = a² + b² - 2ab

then,

$\rm↪ \: \cancel{{x}^{2} }+ \cancel{\frac{1}{ {x}^{2} } } - 2( \cancel{x})( \cancel{\frac{1}{x}} ) = \cancel{{x}^{2} } + \cancel{ \frac{1}{ {x}^{2} }} + a$

$\rm↪ \: \color{pink}a = - 2$

$\over▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄▄$

$\underline{ \purple{ \bf FINAL \: \: ANSWER}} :$

The value of a is -2 .