Question

find the value of this​

Answer 1

Step-by-step explanation:

+1/=7

+=7/1=7

2=7

=7/2

= 3.5

1. ² + 1/ ²
2. (3.5)² + 1/(3.5)²
3. 12.25 + 1 / 12.25 (12.25 on top and down gets canceled )
4. 1 is the ans

ii) ⁴+1/ ⁴

• (3.5)⁴ + 1/ (3.5)⁴
• 150.0625 +1/150.0625 (the no. gets canceled on both the sides at top and bottom)
• 1 is ans

Answer 2

Given :-

$:⟹x + \frac{1}{x} = 7$

To Find :-

$:⟹ {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ :⟹ {x}^{4} + \frac{1}{ {x}^{4} }$

Required Answer :-

⓵

On squaring both sides ,

$:⟹ {(x + \frac{1}{x}) }^{2} = {(7)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ :⟹ {x}^{2} + 2 \times x \times \frac{1}{x} + {( \frac{1}{x} )}^{2} = 49 \\ \\ :⟹ {x}^{2} + 2 + (\frac{ 1}{ {x}^{2} } ) = 49 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ :⟹ {x}^{2} + \frac{1}{ {x}^{2} } = 49 - 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\:⟹ {x}^{2} + \frac{1}{ {x}^{2} } = 47 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

⓶

If we squaring on (x² + 1/x²)² = (7)²

$:⟹ {x}^{2} + \frac{1}{ {x}^{2} } = 49$

so , again on squaring both sides,

$:⟹( {x}^{2} + \frac{1}{ {x}^{2} } )^{2} = {(49)}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ :⟹ {x}^{4} + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } + \frac{1}{ {x}^{4} } = 2209 \\ \\ :⟹ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 2209 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now subtracting 2 from both the sides

$:⟹{x}^{4} + \frac{1}{ {x}^{4} } + 2 - 2= 2209 - 2 \\ \\ :⟹ {x}^{4} + \frac{1}{ {x}^{4} } = 2207 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

I hope it helps you.

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