Question

The value of m^2 + 1/m^2 = 3, then what will be the value of m^8 + 1/m^?
pls answer the above question, it's my practice paper question

Answer 1

Step-by-step explanation:

Corrected Question:-

If m²+(1/m²) = 3 then find the value of m⁸+(1/m⁸) ?

Given :-

m²+(1/m²) = 3

To find :-

The value of m⁸+(1/m⁸)

Solution :-

Given that m²+(1/m²) = 3

On squaring both sides then

=> [m²+(1/m²)]²= 3²

=> (m²)²+(1/m²)²+2(m²)(1/m²) = 3×3

Since, (a+b)² = a²+2ab+b²

Where , a = m² and b = 1/m²

=> m⁴+(1/m⁴)+2(m²/m²) = 9

=> m⁴+(1/m⁴)+2(1) = 9

=> m⁴+(1/m⁴)+2 = 9

=> m⁴+(1/m⁴) = 9 -2

=> m⁴+(1/m⁴) = 7

On squaring both sides again then

=> [m⁴+(1/m⁴)]² = 7²

=> (m⁴)²+(1/m⁴)²+2(m⁴)(1/m⁴) = 7×7

Since, (a+b)² = a²+2ab+b²

Where , a = m⁴ and b = 1/m⁴

=> m⁸+(1/m⁸)+2(m⁴/m⁴) = 49

=> m⁸+(1/m⁸)+2(1) = 49

=> m⁸+(1/m⁸)+2 = 49

=> m⁸+(1/m⁸) = 49-2

Therefore, m⁸+(1/m⁸) = 47

Answer :-

The value of m⁸+(1/m⁸) is 47

Used formulae:-

→ (a+b)² = a²+2ab+b²

Answer 2

Answer:

m⁸ + 1/m⁸ = 47

Step-by-step explanation:

Given :-

${ \boxed{ \sf {m}^{2} + \dfrac{1}{ {m}^{2} } = 3 }}$

To Find :-

${ \boxed{ \sf {m}^{8} + \dfrac{1}{ {m}^{8} }}}$

Solution :-

Given,

m² + 1/m² = 3

On squaring both sides

(m² + 1/m²)² = (3)²

We know that

(a + b)² = a² + b² + 2ab

(m²)² + (1/m²)² + 2 × m² × 1/m² = 9

Since

$\sf \: (a{}^{m})^{n} = {a}^{m \times n}$

m⁴ + 1/m⁴ + 2 × m²/m² = 9

m⁴ + 1/m⁴ + 2 = 9

m⁴ + 1/m⁴ = 9 - 2

m⁴ + 1/m⁴ = 7

Again squaring both sides

(m⁴ + 1/m⁴)² = (7)²

(m⁴)² + (1/m⁴)² + 2 × m⁴ + 1/m⁴ = 49

m⁸ + 1/m⁸ + 2 × m⁴/m⁴ = 49

m⁸ + 1/m⁸ + 2 = 49

m⁸ + 1/m⁸ = 49 - 2

m⁸ + 1/m⁸ = 47