Question

If p-1/P = m , show that p²+1/P² = m²+2
Give me the answer​

Answer 1

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

Given Data:

$\rm: \longmapsto p - \dfrac{1}{p} = m$

On squaring both sides, we get:

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

Using identity (a - b)² = a² - 2ab + b², we get:

$\rm: \longmapsto {p}^{2} - 2 \cdot p \cdot \dfrac{1}{p} + \bigg(\dfrac{1}{p} \bigg)^{2} = {m}^{2}$

$\rm: \longmapsto {p}^{2} - 2 + \dfrac{1}{ {p}^{2} } = {m}^{2}$

Adding 2 to both sides, we get:

$\rm: \longmapsto {p}^{2}+ \dfrac{1}{ {p}^{2} } = {m}^{2} + 2$

Hence Proved..!!

$\textsf{\large{\underline{Learn More}:}}$

1. (a + b)² = a² + 2ab + b²
2. (a - b)² = a² - 2ab + b²
3. a² - b² = (a + b)(a - b)
4. (a + b)³ = a³ + 3ab(a + b) + b³
5. (a - b)³ = a³ - 3ab(a - b) - b³
6. a³ + b³ = (a + b)(a² - ab + b²)
7. a³ - b³ = (a - b)(a² + ab + b²)