Question

if x(x-2)=1,then find the value of x*x+1/x*x​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given That:

$\rm: \longmapsto x(x - 2) = 1$

$\rm: \longmapsto (x - 2) = \dfrac{1}{x}$

$\rm: \longmapsto x -\dfrac{1}{x} = 2$

Squaring both sides, we get:

$\rm: \longmapsto \bigg(x -\dfrac{1}{x} \bigg)^{2} = 4$

We know that:

$\rm: \longmapsto {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

Therefore:

$\rm: \longmapsto {x}^{2} + \dfrac{1}{ {x}^{2} } - 2 = 4$

$\rm: \longmapsto {x}^{2} + \dfrac{1}{ {x}^{2} } = 6$

★ Which is our required answer.

$\textsf{\large{\underline{More Identities To Know}:}}$

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)