If x-1-x-1-2- then write the value of 4x2-4-x2-

X 1/x=1/2 2x 2/x=1 (Multiplying by 2) Squaring both sides, (2x 2/x)^2=(1)^2 ⇒ 4x^2+4/x^2 2× 2x ×2/x=1 ⇒ 4x^2+4/x^2 8=1 ⇒ 4x^2+4/x^2=1+8=9 ∴ 4x^2+4/x^2=9 ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If x-1/x=1/2,...

Question

If $x - \frac{1}{x} = \frac{1}{2}$ , then write the value of $4 x^{2} + \frac{4}{x^{2}}$ .

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Solution

$x - \frac{1}{x} = \frac{1}{2} 2 x - \frac{2}{x} = 1 (Multiplying by 2) Squaring both sides, {(2 x - \frac{2}{x})}^{2} = (1)^{2} \Rightarrow 4 x^{2} + \frac{4}{x^{2}} - 2 \times 2 x \times \frac{2}{x} = 1 \Rightarrow 4 x^{2} + \frac{4}{x^{2}} - 8 = 1 \Rightarrow 4 x^{2} + \frac{4}{x^{2}} = 1 + 8 = 9 ∴ 4 x^{2} + \frac{4}{x^{2}} = 9$

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If x−1x=12, then write the value of 4x2+4x2.

x−1x=122x−2x=1 (Multiplying by 2)Squaring both sides,(2x−2x)2=(1)2⇒ 4x2+4x2−2×2x×2x=1⇒ 4x2+4x2−8=1⇒ 4x2+4x2=1+8=9∴ 4x2+4x2=9

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