Question

Explain step by step​

Answer 1

EXPLANATION.

⇒ (x + 1/x) = 5.

As we know that,

Squaring on both sides of the equation, we get.

⇒ (x + 1/x)² = (5)².

As we know that,

Formula of :

⇒ (a + b)² = a² + b² + 2ab.

Using this formula in the equation, we get.

⇒ (x)² + (1/x)² + 2(x)(1/x) = 25.

⇒ x² + 1/x² + 2 = 25.

⇒ x² + 1/x² = 25 - 2.

⇒ x² + 1/x² = 23.

Answer 2

Answer:

${\implies}{ \boxed{\mathbb{\red{given \: that }}}}\\ x + \frac{1}{x} = 5 \: \: - (1) \\ find \\ {x}^{2} + \frac{1}{x {}^{2} } \\ {\implies}{ {\mathbb{\blue{squarring \: both \: side \: in \: equation \: (1) }}}}\\ (x + \frac{1}{x} ) {}^{2} = (5) {}^{2} \\ using \: identity \\ \:{\implies}{ \boxed{\mathbb{\pink{( a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab \: \: we \: get}}}} \\(5) { }^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2 \times x \times \frac{1}{x} \\ 25 = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ 25 - 2 = {x}^{2} + \frac{1}{ {x}^{2} } \\ {\implies}{{\mathbb{\green{23 = {x}^{2} + \frac{1}{ {x}^{2} } }}}}$

Step-by-step explanation: