Question

if 2x + 1/2x =9 find 4x'2 + 1/4x'2


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Answer 1

⇒ (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

Answer 2

$(2x + \frac{1}{2} x) ^{2} = (2 {x}^{2} ) + (\frac{1}{2} ) ^{2} + 2 \times 2x \times \frac{1}{2} x \\ (9) {}^{2} = 4 {x}^{2} + \frac{1}{4} {x}^{2} + 2 \\ 81 = 4 {x}^{2} + \frac{1}{4} {x}^{2} + 2 \\ 4 {x}^{2} + \frac{1}{4} {x}^{2} = 81 - 2 \\ 4 {x}^{2} + \frac{1}{4} {x}^{2} = 79$