Question

If m+1\m = 6. Find the value of m^4 + 1/m^4

Answer 1

$hey....$
$m + \frac{1}{m} = 6 \\ (m + \frac{1}{m} ) {}^{2} = (6) {}^{2}$
${m}^{2} + \frac{1}{ {m}^{2} } + (2 \times m \times \frac{1}{m)} = 36$
${m}^{2} + \frac{1}{ {m}^{2} } = 36 - 2 \\ \\ {m}^{2} + \frac{1}{ {m}^{2} } = 34$
$( {m}^{2} + \frac{1}{ {m}^{2} } ) {}^{2} = (34) ^{2}$
${m}^{4} + \frac{1}{ {m}^{4} } = 1156 - 2 \\ \\ {m}^{4} + \frac{1}{ {m}^{4} } = 1154$
$thank \: you$

Answer 2

Hi ☺ !!

Here is your answer ✓ ✓ ✓ ✓

M + 1/M = 6

Squaring both sides , we get

( m + 1/m)² = 6²

m² + 1/m² + 2 × ( m × 1/m ) = 36

m² + 1/m² + 2 = 36

m² + 1/m² = 36 - 2

m² + 1/m² = 34.

Now , squaring both sides again , we get

( m² + 1/m² )² = 34²

m⁴ + 1/m⁴ + 2 ( m² × 1/m² ) = 1156

m⁴ + 1/m⁴ + 2 = 1156

m⁴ + 1/m⁴ = 1156 - 2

m⁴ + 1/m⁴ = 1154.

☺ Hope it will help you ☺

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