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The Brainliest Answer!

(i)4x² + 1/4x² =?

2x-1/2x=4

(2x-1/2x)² = 4² [Squaring on both sides]

(2x)² + (1/2x)² - (2*2x*1/2x) = 16 [(a-b)² = a² + b² - 2*a*b ]

4x² + 1/4x² - 2 = 16 [2x * 1/2x = 1]

4x² + 1/4x² = 16+2

4x² + 1/4x² = 18

(ii)8x³ - 1/8x³ =?

2x - 1/2x = 4

(2x - 1/2x)³ = 4³ [Cubing on both sides]

(2x)³ - (1/2x)³ - 3*2x*1/2x(2x - 1/2x) = 64 [(a-b)³ = a³ - b³ - 3*a*b(a-b)]

8x³ - 1/8x³ - 3(2x - 1/2x) = 64 [2x * 1/2x = 1]

8x³ - 1/8x³ - 3*4 = 64 [2x - 1/2x = 4. Also from equation (iii)]

8x³ - 1/8x³ - 12 = 64

8x³ - 1/8x³ = 64+12

8x³ - 1/8x³ = 76