Question

if a-1 = 3 find a ²+1


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Answer 1

Please mark me as brainliest and hope it helps

Answer 2

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

Given that:

$\rm:\longmapsto a + \dfrac{1}{a} = 7$

Squaring both sides, we get:

$\rm:\longmapsto\bigg(a+\dfrac{1}{a}\bigg)^{2}={7}^{2}$

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

$\rm:\longmapsto {a}^{2} +\dfrac{1}{ {a}^{2} } + 2\cdot a\cdot \dfrac{1}{a} =49$

$\rm:\longmapsto {a}^{2} +\dfrac{1}{ {a}^{2} } + 2=49$

Subtracting 2 from both sides, we get:

$\rm:\longmapsto {a}^{2} +\dfrac{1}{ {a}^{2} }=49 -2$

$\rm:\longmapsto {a}^{2} +\dfrac{1}{ {a}^{2} }=47$

★ So, the value of a² + 1/a² is 47.

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

• a² + 1/a² = 47.

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

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