Question

2x + 1 / 2x = 5 find 4x square + 1 / 4x square ​

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Answer 1

Step-by-step explanation:

(i) 2x – (1/2x) = 4

⇒ (2x – (1/2x)) 2 = (4)2

⇒ (2x)2 + (1/2x)2 – 2 × 2x × (1/2x) = 16

⇒ 4x2 + (1/4x2) - 2 = 16

⇒ 4x2 + (1/4x2) = 16 + 2

⇒ 4x2 + (1/4x2) = 18

(ii) 2x – (1/2x) = 4

⇒ (2x – 1/2x)3 = (4)3

⇒ (2x)3 – (1/2x)3 – 3 × 2x × (1/2x) (2x – (1/2x)) = 64

⇒ 8x3 – (1/8x3) – 3(4) = 64

⇒ 8x3 – (1/8x3) – 12 = 64

⇒ 8x3 – (1/8x3) = 64 + 12 ⇒ 8x3 – (1/8x3) = 76.

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Answer 2

Given -

2x + ½x = 5 .

To find -

Find the value of -

=> 4x² + ¼x² .

Solution -

2x + ½x = 5 .

Now , we know what -

( a + b )² = a² + 2ab + b² .

So , squaring this -

2x + ½x = 5

=> [ 2x + ½x ]² = 5²

=> 4x² + ¼x² + 2 = 25

=> 4x² + ¼x² = 23 .

This is the required answer .

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Additional Information -

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

( a + b )( a - b ) = a² - b²

( a + b )³ = a³ + 3ab ( a + b ) + b³

( a - b )³ = a³ - 3ab ( a + b ) - b³

( a + b + c )³ = a³ + b³ + c³ + 3 ( a + b )( b + c )( c + a )

a³ + b³ + c³ - 3abc = ( a + b + c )( a² + b² + c² - ab - bc - ca )

When a + b + c = 0 ,

a³ + b³ + c³ = 3abc .

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